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Saçu İE. Dynamics and synchronization control of fractional conformable neuron system. Cogn Neurodyn 2024; 18:247-263. [PMID: 39170599 PMCID: PMC11333422 DOI: 10.1007/s11571-023-09933-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2022] [Revised: 11/25/2022] [Accepted: 01/09/2023] [Indexed: 02/09/2023] Open
Abstract
Dynamic analysis, electrical coupling and synchronization control of the conformable FitzHugh-Nagumo neuronal models have been presented in this work. Firstly, equations of the Adomian-Decomposition-Method and conformable neuron model have been introduced. The Adomian-Decomposition-Method has been employed for the numerical simulation analysis, since it converges fast and provides serial solutions. Fractional order and external current stimulus have been considered as bifurcation parameters and their effects on neuron model dynamics have been examined in detail. Then, the electrical coupling of the two conformable neuronal models without any controller has been revealed and the significance of the coupling strength parameter has been evaluated. To eliminate impact of the coupling strength parameter on synchronization status of neurons, Lyapunov control method has been employed for synchronization control. In the last step, the numerical simulation studies have been experimentally verified using the Texas Instrument Delfino digital signal processor board. Numerical simulation results together with experimental validation have showed that the types of dynamics of the related neuron model are not affected from the change of the fractional order of conformable derivative, but the frequency of the dynamic response of the neuronal model is changed from the alteration of the fractional order. The frequency of response of the neuron model increases with decreasing values of the fractional order. On the other hand, if there is no synchronization control method, the coupled neuron models exhibit response ranging from synchronous to asynchronous depending on the sign and value of the coupling parameter. Additionally, decreasing values of the fractional order may allow the coupled neurons to enter the synchronous state more quickly due to increasing frequency of response of the neuronal model. Finally, the coupled neuron models could exhibit synchronous behavior, that is determined by calculating the standard deviation results, regardless of the value of the coupling parameter by using the Lyapunov control method.
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Affiliation(s)
- İbrahim Ethem Saçu
- Clinical Engineering Research and Implementation Center (ERKAM), Erciyes University, 38030 Kayseri, Turkey
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2
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Souza DLM, Gabrick EC, Protachevicz PR, Borges FS, Trobia J, Iarosz KC, Batista AM, Caldas IL, Lenzi EK. Adaptive exponential integrate-and-fire model with fractal extension. CHAOS (WOODBURY, N.Y.) 2024; 34:023107. [PMID: 38341761 DOI: 10.1063/5.0176455] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2023] [Accepted: 01/08/2024] [Indexed: 02/13/2024]
Abstract
The description of neuronal activity has been of great importance in neuroscience. In this field, mathematical models are useful to describe the electrophysical behavior of neurons. One successful model used for this purpose is the Adaptive Exponential Integrate-and-Fire (Adex), which is composed of two ordinary differential equations. Usually, this model is considered in the standard formulation, i.e., with integer order derivatives. In this work, we propose and study the fractal extension of Adex model, which in simple terms corresponds to replacing the integer derivative by non-integer. As non-integer operators, we choose the fractal derivatives. We explore the effects of equal and different orders of fractal derivatives in the firing patterns and mean frequency of the neuron described by the Adex model. Previous results suggest that fractal derivatives can provide a more realistic representation due to the fact that the standard operators are generalized. Our findings show that the fractal order influences the inter-spike intervals and changes the mean firing frequency. In addition, the firing patterns depend not only on the neuronal parameters but also on the order of respective fractal operators. As our main conclusion, the fractal order below the unit value increases the influence of the adaptation mechanism in the spike firing patterns.
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Affiliation(s)
- Diogo L M Souza
- Graduate Program in Science, State University of Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil
| | - Enrique C Gabrick
- Graduate Program in Science, State University of Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil
- Department of Physics, Humboldt University Berlin, Newtonstraße 15, 12489 Berlin, Germany
- Potsdam Institute for Climate Impact Research, Telegrafenberg A31, 14473 Potsdam, Germany
| | | | - Fernando S Borges
- Department of Physiology and Pharmacology, State University of New York Downstate Health Sciences University, Brooklyn, New York 11203, USA
- Center for Mathematics, Computation, and Cognition, Federal University of ABC, 09606-045 São Bernardo do Campo, SP, Brazil
| | - José Trobia
- Department of Mathematics and Statistics, State University of Ponta Grossa, 84030-900 Ponta Grossa, Brazil
| | - Kelly C Iarosz
- University Center UNIFATEB, 84266-010 Telêmaco Borba, PR, Brazil
| | - Antonio M Batista
- Graduate Program in Science, State University of Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil
- Institute of Physics, University of São Paulo, 05508-090 São Paulo, SP, Brazil
- Department of Mathematics and Statistics, State University of Ponta Grossa, 84030-900 Ponta Grossa, Brazil
| | - Iberê L Caldas
- Institute of Physics, University of São Paulo, 05508-090 São Paulo, SP, Brazil
| | - Ervin K Lenzi
- Graduate Program in Science, State University of Ponta Grossa, 84030-900 Ponta Grossa, PR, Brazil
- Departament of Physics, State University of Ponta Grossa, Av. Gen. Carlos Cavalcanti 4748, Ponta Grossa 84030-900, PR, Brazil
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Sharma SK, Mondal A, Kaslik E, Hens C, Antonopoulos CG. Diverse electrical responses in a network of fractional-order conductance-based excitable Morris-Lecar systems. Sci Rep 2023; 13:8215. [PMID: 37217514 DOI: 10.1038/s41598-023-34807-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2022] [Accepted: 05/08/2023] [Indexed: 05/24/2023] Open
Abstract
The diverse excitabilities of cells often produce various spiking-bursting oscillations that are found in the neural system. We establish the ability of a fractional-order excitable neuron model with Caputo's fractional derivative to analyze the effects of its dynamics on the spike train features observed in our results. The significance of this generalization relies on a theoretical framework of the model in which memory and hereditary properties are considered. Employing the fractional exponent, we first provide information about the variations in electrical activities. We deal with the 2D class I and class II excitable Morris-Lecar (M-L) neuron models that show the alternation of spiking and bursting features including MMOs & MMBOs of an uncoupled fractional-order neuron. We then extend the study with the 3D slow-fast M-L model in the fractional domain. The considered approach establishes a way to describe various characteristics similarities between fractional-order and classical integer-order dynamics. Using the stability and bifurcation analysis, we discuss different parameter spaces where the quiescent state emerges in uncoupled neurons. We show the characteristics consistent with the analytical results. Next, the Erdös-Rényi network of desynchronized mixed neurons (oscillatory and excitable) is constructed that is coupled through membrane voltage. It can generate complex firing activities where quiescent neurons start to fire. Furthermore, we have shown that increasing coupling can create cluster synchronization, and eventually it can enable the network to fire in unison. Based on cluster synchronization, we develop a reduced-order model which can capture the activities of the entire network. Our results reveal that the effect of fractional-order depends on the synaptic connectivity and the memory trace of the system. Additionally, the dynamics captures spike frequency adaptation and spike latency that occur over multiple timescales as the effects of fractional derivative, which has been observed in neural computation.
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Affiliation(s)
- Sanjeev K Sharma
- Department of Mathematics, VIT-AP University, Amaravati, 522237, Andhra Pradesh, India
| | - Argha Mondal
- Department of Mathematics, Sidho-Kanho-Birsha University, Purulia, 723104, West Bengal, India.
- Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester, UK.
| | - Eva Kaslik
- Department of Mathematics and Computer Science, West University of Timisoara, Timisoara, Romania.
- Institute for Advanced Environmental Research, West University of Timisoara, Timisoara, Romania.
| | | | - Chris G Antonopoulos
- Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester, UK.
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Lu Q, Wang X, Tian J. A new biological central pattern generator model and its relationship with the motor units. Cogn Neurodyn 2022; 16:135-147. [PMID: 35126774 PMCID: PMC8807781 DOI: 10.1007/s11571-021-09710-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2021] [Revised: 06/27/2021] [Accepted: 07/31/2021] [Indexed: 02/03/2023] Open
Abstract
The central pattern generator (CPG) is a key neural-circuit component of the locomotion control system. Recently, numerous molecular and genetic approaches have been proposed for investigating the CPG mechanisms. The rhythm in the CPG locomotor circuits comes from the activity in the ipsilateral excitatory neurons whose output is controlled by inter-neuron inhibitory connections. Conventional models for simulating the CPG mechanism are complex Hodgkin-Huxley-type models. Inspired by biological investigations and the continuous-time Matsuoka model, we propose new integral-order and fractional-order CPG models, which consider time delays and synaptic interfaces. The phase diagrams exhibit limit cycles and periodic solutions, in agreement with the CPG biological characteristics. As well, the fractional-order model shows state transitions with order variations. In addition, we investigate the relationship between the CPG and the motor units through the construction of integral-order and fractional-order coupling models. Simulations of these coupling models show that the states generated by the three motor units are in accordance with the experimentally-obtained states in previous studies. The proposed models reveal that the CPG can regulate limb locomotion patterns through connection weights and synaptic interfaces. Moreover, in comparison to the integral-order models, the fractional-order ones appear to be more effective, and hence more suitable for describing the dynamics of the CPG biological system.
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Affiliation(s)
- Qiang Lu
- College of Medical Information Engineering, Shandong First Medical University & Shandong Academy of Medical Sciences, Taian, 271000 China
| | - Xiaoyan Wang
- College of Medical Information Engineering, Shandong First Medical University & Shandong Academy of Medical Sciences, Taian, 271000 China
| | - Juan Tian
- College of Medical Information Engineering, Shandong First Medical University & Shandong Academy of Medical Sciences, Taian, 271000 China
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5
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Janzakova K, Ghazal M, Kumar A, Coffinier Y, Pecqueur S, Alibart F. Dendritic Organic Electrochemical Transistors Grown by Electropolymerization for 3D Neuromorphic Engineering. ADVANCED SCIENCE (WEINHEIM, BADEN-WURTTEMBERG, GERMANY) 2021; 8:e2102973. [PMID: 34716682 PMCID: PMC8693061 DOI: 10.1002/advs.202102973] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2021] [Revised: 09/13/2021] [Indexed: 05/16/2023]
Abstract
One of the major limitations of standard top-down technologies used in today's neuromorphic engineering is their inability to map the 3D nature of biological brains. Here, it is shown how bipolar electropolymerization can be used to engineer 3D networks of PEDOT:PSS dendritic fibers. By controlling the growth conditions of the electropolymerized material, it is investigated how dendritic fibers can reproduce structural plasticity by creating structures of controllable shape. Gradual topologies evolution is demonstrated in a multielectrode configuration. A detailed electrical characterization of the PEDOT:PSS dendrites is conducted through DC and impedance spectroscopy measurements and it is shown how organic electrochemical transistors (OECT) can be realized with these structures. These measurements reveal that quasi-static and transient response of OECTs can be adjusted by controlling dendrites' morphologies. The unique properties of organic dendrites are used to demonstrate short-term, long-term, and structural plasticity, which are essential features required for future neuromorphic hardware development.
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Affiliation(s)
- Kamila Janzakova
- Institut d’ÉlectroniqueMicroélectronique et Nanotechnologies (IEMN) ‐ CNRS UMR 8520 ‐ Université de Lilleboulevard PoincarréVilleneuve d'Ascq59652France
| | - Mahdi Ghazal
- Institut d’ÉlectroniqueMicroélectronique et Nanotechnologies (IEMN) ‐ CNRS UMR 8520 ‐ Université de Lilleboulevard PoincarréVilleneuve d'Ascq59652France
| | - Ankush Kumar
- Institut d’ÉlectroniqueMicroélectronique et Nanotechnologies (IEMN) ‐ CNRS UMR 8520 ‐ Université de Lilleboulevard PoincarréVilleneuve d'Ascq59652France
| | - Yannick Coffinier
- Institut d’ÉlectroniqueMicroélectronique et Nanotechnologies (IEMN) ‐ CNRS UMR 8520 ‐ Université de Lilleboulevard PoincarréVilleneuve d'Ascq59652France
| | - Sébastien Pecqueur
- Institut d’ÉlectroniqueMicroélectronique et Nanotechnologies (IEMN) ‐ CNRS UMR 8520 ‐ Université de Lilleboulevard PoincarréVilleneuve d'Ascq59652France
| | - Fabien Alibart
- Institut d’ÉlectroniqueMicroélectronique et Nanotechnologies (IEMN) ‐ CNRS UMR 8520 ‐ Université de Lilleboulevard PoincarréVilleneuve d'Ascq59652France
- Laboratoire Nanotechnologies Nanosystèmes (LN2) ‐ CNRS UMI‐3463 ‐ 3ITSherbrookeJ1K 0A5Canada
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6
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Allagui A, Elwakil AS. Possibility of information encoding/decoding using the memory effect in fractional-order capacitive devices. Sci Rep 2021; 11:13306. [PMID: 34172771 PMCID: PMC8233438 DOI: 10.1038/s41598-021-92568-3] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2021] [Accepted: 06/14/2021] [Indexed: 11/29/2022] Open
Abstract
In this study, we show that the discharge voltage pattern of a supercapacitor exhibiting fractional-order behavior from the same initial steady-state voltage into a constant resistor is dependent on the past charging voltage profile. The charging voltage was designed to follow a power-law function, i.e. \documentclass[12pt]{minimal}
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\begin{document}$$t_{ss}$$\end{document}tss (charging time duration between zero voltage to the terminal voltage \documentclass[12pt]{minimal}
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\begin{document}$$0<p<1$$\end{document}0<p<1) act as two variable parameters. We used this history-dependence of the dynamic behavior of the device to uniquely retrieve information pre-coded in the charging waveform pattern. Furthermore, we provide an analytical model based on fractional calculus that explains phenomenologically the information storage mechanism. The use of this intrinsic material memory effect may lead to new types of methods for information storage and retrieval.
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Affiliation(s)
- Anis Allagui
- Department of Sustainable and Renewable Energy Engineering, University of Sharjah, PO Box 27272, Sharjah, United Arab Emirates. .,Research Institute of Sciences and Engineering, University of Sharjah, PO Box 27272, Sharjah, United Arab Emirates. .,Department of Mechanical and Materials Engineering, Florida International University, Miami, FL, 33174, USA.
| | - Ahmed S Elwakil
- Department of Electrical Engineering, University of Sharjah, PO Box 27272, Sharjah, United Arab Emirates.,Nanoelectronics Integrated Systems Center, Nile University, Cairo, 12588, Egypt.,Department of Electrical and Computer Engineering, University of Calgary, Calgary, Alberta, T2N 1N4, Canada
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7
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Mankin R, Rekker A, Paekivi S. Statistical moments of the interspike intervals for a neuron model driven by trichotomous noise. Phys Rev E 2021; 103:062201. [PMID: 34271748 DOI: 10.1103/physreve.103.062201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2021] [Accepted: 05/14/2021] [Indexed: 11/07/2022]
Abstract
The influence of a colored three-level input noise (trichotomous noise) on the spike generation of a perfect integrate-and-fire (PIF) model of neurons is studied. Using a first-passage-time formulation, exact expressions for the Laplace transform of the output interspike interval (ISI) density and for the statistical moments of the ISIs (such as the coefficient of variation, the skewness, the serial correlation coefficient, and the Fano factor) are derived. To model the anomalous subdiffusion that can arise from, e.g., the trapping properties of dendritic spines, the model is extended by including a random operational time in the form of an inverse strictly increasing Lévy-type subordinator, and exact formulas for ISI statistics are given for this case as well. Particularly, it is shown that at some parameter regimes, the ISI density exhibits a three-modal structure. The results for the extended model show that the ISI serial correlation coefficient and the Fano factor are nonmonotonic with respect to the input current, which indicates that at an intermediate value of the input current the variability of the output spike trains is minimal. Similarities and differences between the behavior of the presented models and the previously investigated PIF models driven by dichotomous noise are also discussed.
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Affiliation(s)
- Romi Mankin
- School of Natural Sciences and Health, Tallinn University, 29 Narva Road, 10120 Tallinn, Estonia
| | - Astrid Rekker
- School of Natural Sciences and Health, Tallinn University, 29 Narva Road, 10120 Tallinn, Estonia
| | - Sander Paekivi
- School of Natural Sciences and Health, Tallinn University, 29 Narva Road, 10120 Tallinn, Estonia
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8
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Sharma SK, Mondal A, Mondal A, Upadhyay RK, Hens C. Emergence of bursting in a network of memory dependent excitable and spiking leech-heart neurons. J R Soc Interface 2020; 17:20190859. [PMID: 32574543 DOI: 10.1098/rsif.2019.0859] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
Excitable cells often produce different oscillatory activities that help us to understand the transmitting and processing of signals in the neural system. The diverse excitabilities of an individual neuron can be reproduced by a fractional-order biophysical model that preserves several previous memory effects. However, it is not completely clear to what extent the fractional-order dynamics changes the firing properties of excitable cells. In this article, we investigate the alternation of spiking and bursting phenomena of an uncoupled and coupled fractional leech-heart (L-H) neurons. We show that a complete graph of heterogeneous de-synchronized neurons in the backdrop of diverse memory settings (a mixture of integer and fractional exponents) can eventually lead to bursting with the formation of cluster synchronization over a certain threshold of coupling strength, however, the uncoupled L-H neurons cannot reveal bursting dynamics. Using the stability analysis in fractional domain, we demarcate the parameter space where the quiescent or steady-state emerges in uncoupled L-H neuron. Finally, a reduced-order model is introduced to capture the activities of the large network of fractional-order model neurons.
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Affiliation(s)
- Sanjeev Kumar Sharma
- Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, India
| | - Argha Mondal
- Computational Neuroscience Center, University of Washington, Seattle, WA, USA.,Physics and Applied Mathematics Unit, Indian Statistical Institute, BT Road, Kolkata 700108, India
| | - Arnab Mondal
- Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, India
| | - Ranjit Kumar Upadhyay
- Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, India
| | - Chittaranjan Hens
- Physics and Applied Mathematics Unit, Indian Statistical Institute, BT Road, Kolkata 700108, India
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Lu Q. Dynamics and coupling of fractional-order models of the motor cortex and central pattern generators. J Neural Eng 2020; 17:036021. [PMID: 32344390 DOI: 10.1088/1741-2552/ab8dd6] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
OBJECTIVE Fractional calculus plays a key role in the analysis of neural dynamics. In particular, fractional calculus has been recently exploited for analyzing complex biological systems and capturing intrinsic phenomena. Also, artificial neural networks have been shown to have complex neuronal dynamics and characteristics that can be modeled by fractional calculus. Moreover, for a neural microcircuit placed on the spinal cord, fractional calculus can be employed to model the central pattern generator (CPG). However, the relation between the CPG and the motor cortex is still unclear. APPROACH In this paper, fractional-order models of the CPG and the motor cortex are built on the Van der Pol oscillator and the neural mass model (NMM), respectively. A self-consistent mean field approximation is used to construct the potential landscape of the Van der Pol oscillator. This landscape provides a useful tool to observe the 3D dynamics of the oscillator. To infer the relation of the motor cortex and CPG, the coupling model between the fractional-order Van der Pol oscillator and the NMM is built. As well, the influence of the coupling parameters on the CPG and the motor cortex is assessed. MAIN RESULTS Fractional-order NMM and coupling model of the motor cortex and the CPG are first established. The potential landscape is used to show 3D probabilistic evolution of the Van der Pol oscillator states. Detailed observations of the evolution of the system states can be made with fractional calculus. In particular, fractional calculus enables the observation of the creation of stable modes and switching between them. SIGNIFICANCE The results confirm that the motor cortex and CPG have associated modes or states that can be switched based on changes in the fractional order and the time delay. Fractional calculus and the potential landscape are helpful methods for better understanding of the working principles of locomotion systems.
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Affiliation(s)
- Qiang Lu
- College of Medical Information Engineering, Shandong First Medical University & Shandong Academy of Medical Sciences, Taian 271000, People's Republic of China
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10
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Abstract
The aim of this paper is the construction of stochastic versions for some fractional Gompertz curves. To do this, we first study a class of linear fractional-integral stochastic equations, proving existence and uniqueness of a Gaussian solution. Such kinds of equations are then used to construct fractional stochastic Gompertz models. Finally, a new fractional Gompertz model, based on the previous two, is introduced and a stochastic version of it is provided.
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Fractional Ornstein-Uhlenbeck Process with Stochastic Forcing, and its Applications. Methodol Comput Appl Probab 2019. [DOI: 10.1007/s11009-019-09748-y] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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12
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Mondal A, Sharma SK, Upadhyay RK, Mondal A. Firing activities of a fractional-order FitzHugh-Rinzel bursting neuron model and its coupled dynamics. Sci Rep 2019; 9:15721. [PMID: 31673009 PMCID: PMC6823374 DOI: 10.1038/s41598-019-52061-4] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2018] [Accepted: 09/17/2019] [Indexed: 12/13/2022] Open
Abstract
Fractional-order dynamics of excitable systems can be physically described as a memory dependent phenomenon. It can produce diverse and fascinating oscillatory patterns for certain types of neuron models. To address these characteristics, we consider a nonlinear fast-slow FitzHugh-Rinzel (FH-R) model that exhibits elliptic bursting at a fixed set of parameters with a constant input current. The generalization of this classical order model provides a wide range of neuronal responses (regular spiking, fast-spiking, bursting, mixed-mode oscillations, etc.) in understanding the single neuron dynamics. So far, it is not completely understood to what extent the fractional-order dynamics may redesign the firing properties of excitable systems. We investigate how the classical order system changes its complex dynamics and how the bursting changes to different oscillations with stability and bifurcation analysis depending on the fractional exponent (0 < α ≤ 1). This occurs due to the memory trace of the fractional-order dynamics. The firing frequency of the fractional-order FH-R model is less than the classical order model, although the first spike latency exists there. Further, we investigate the responses of coupled FH-R neurons with small coupling strengths that synchronize at specific fractional-orders. The interesting dynamical characteristics suggest various neurocomputational features that can be induced in this fractional-order system which enriches the functional neuronal mechanisms.
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Affiliation(s)
- Argha Mondal
- Computational Neuroscience Center, University of Washington, Seattle, Washington, USA
| | - Sanjeev Kumar Sharma
- Department of Mathematics & Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad, 826004, India
| | - Ranjit Kumar Upadhyay
- Department of Mathematics & Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad, 826004, India.
| | - Arnab Mondal
- Department of Mathematics & Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad, 826004, India
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13
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Pirozzi E. Colored noise and a stochastic fractional model for correlated inputs and adaptation in neuronal firing. BIOLOGICAL CYBERNETICS 2018; 112:25-39. [PMID: 28864925 DOI: 10.1007/s00422-017-0731-0] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2017] [Accepted: 08/18/2017] [Indexed: 06/07/2023]
Abstract
High variability in the neuronal response to stimulations and the adaptation phenomenon cannot be explained by the standard stochastic leaky integrate-and-fire model. The main reason is that the uncorrelated inputs involved in the model are not realistic. There exists some form of dependency between the inputs, and it can be interpreted as memory effects. In order to include these physiological features in the standard model, we reconsider it with time-dependent coefficients and correlated inputs. Due to its hard mathematical tractability, we perform simulations of it for a wide investigation of its output. A Gauss-Markov process is constructed for approximating its non-Markovian dynamics. The first passage time probability density of such a process can be numerically evaluated, and it can be used to fit the histograms of simulated firing times. Some estimates of the moments of firing times are also provided. The effect of the correlation time of the inputs on firing densities and on firing rates is shown. An exponential probability density of the first firing time is estimated for low values of input current and high values of correlation time. For comparison, a simulation-based investigation is also carried out for a fractional stochastic model that allows to preserve the memory of the time evolution of the neuronal membrane potential. In this case, the memory parameter that affects the firing activity is the fractional derivative order. In both models an adaptation level of spike frequency is attained, even if along different modalities. Comparisons and discussion of the obtained results are provided.
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Affiliation(s)
- Enrica Pirozzi
- Dipartimento di Matematica e Applicazioni, Università di Napoli FEDERICO II, Via Cintia, 80126, Naples, Italy.
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