1
|
Brice Azangue A, Megam Ngouonkadi EB, Kabong Nono M, Fotsin HB, Sone Ekonde M, Yemele D. Stability and synchronization in neural network with delayed synaptic connections. CHAOS (WOODBURY, N.Y.) 2024; 34:013117. [PMID: 38215223 DOI: 10.1063/5.0175408] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2023] [Accepted: 12/04/2023] [Indexed: 01/14/2024]
Abstract
In this paper, we investigate the stability of the synchronous state in a complex network using the master stability function technique. We use the extended Hindmarsh-Rose neuronal model including time delayed electrical, chemical, and hybrid couplings. We find the corresponding master stability equation that describes the whole dynamics for each coupling mode. From the maximum Lyapunov exponent, we deduce the stability state for each coupling mode. We observe that for electrical coupling, there exists a mixing between stable and unstable states. For a good setting of some system parameters, the position and the size of unstable areas can be modified. For chemical coupling, we observe difficulties in having a stable area in the complex plane. For hybrid coupling, we observe a stable behavior in the whole system compared to the case where these couplings are considered separately. The obtained results for each coupling mode help to analyze the stability state of some network topologies by using the corresponding eigenvalues. We observe that using electrical coupling can involve a full or partial stability of the system. In the case of chemical coupling, unstable states are observed whereas in the case of hybrid interactions a full stability of the network is obtained. Temporal analysis of the global synchronization is also done for each coupling mode, and the results show that when the network is stable, the synchronization is globally observed, while in the case when it is unstable, its nodes are not globally synchronized.
Collapse
Affiliation(s)
- A Brice Azangue
- Research Unit of Condensed Matter, Electronics and Signal Processing, Department of Physics, Faculty of Science, University of Dschang, P.O. Box 067 Dschang, Cameroon
| | - E B Megam Ngouonkadi
- Research Unit of Condensed Matter, Electronics and Signal Processing, Department of Physics, Faculty of Science, University of Dschang, P.O. Box 067 Dschang, Cameroon
- Department of Electrical and Electronic Engineering, College of Technology (COT), University of Buea, P.O. Box 63 Buea, Cameroon
| | - M Kabong Nono
- Research Unit of Condensed Matter, Electronics and Signal Processing, Department of Physics, Faculty of Science, University of Dschang, P.O. Box 067 Dschang, Cameroon
| | - H B Fotsin
- Research Unit of Condensed Matter, Electronics and Signal Processing, Department of Physics, Faculty of Science, University of Dschang, P.O. Box 067 Dschang, Cameroon
| | - M Sone Ekonde
- Department of Electrical and Electronic Engineering, College of Technology (COT), University of Buea, P.O. Box 63 Buea, Cameroon
| | - D Yemele
- Research Unit of Mechanics and Modeling of Physical Systems, Department of Physics, Faculty of Sciences, University of Dschang, P.O. Box 067 Dschang, Cameroon
| |
Collapse
|
2
|
Al-Darabsah I, Chen L, Nicola W, Campbell SA. The Impact of Small Time Delays on the Onset of Oscillations and Synchrony in Brain Networks. Front Syst Neurosci 2021; 15:688517. [PMID: 34290593 PMCID: PMC8287421 DOI: 10.3389/fnsys.2021.688517] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2021] [Accepted: 05/31/2021] [Indexed: 11/13/2022] Open
Abstract
The human brain constitutes one of the most advanced networks produced by nature, consisting of billions of neurons communicating with each other. However, this communication is not in real-time, with different communication or time-delays occurring between neurons in different brain areas. Here, we investigate the impacts of these delays by modeling large interacting neural circuits as neural-field systems which model the bulk activity of populations of neurons. By using a Master Stability Function analysis combined with numerical simulations, we find that delays (1) may actually stabilize brain dynamics by temporarily preventing the onset to oscillatory and pathologically synchronized dynamics and (2) may enhance or diminish synchronization depending on the underlying eigenvalue spectrum of the connectivity matrix. Real eigenvalues with large magnitudes result in increased synchronizability while complex eigenvalues with large magnitudes and positive real parts yield a decrease in synchronizability in the delay vs. instantaneously coupled case. This result applies to networks with fixed, constant delays, and was robust to networks with heterogeneous delays. In the case of real brain networks, where the eigenvalues are predominantly real, owing to the nearly symmetric nature of these weight matrices, biologically plausible, small delays, are likely to increase synchronization, rather than decreasing it.
Collapse
Affiliation(s)
- Isam Al-Darabsah
- Department of Mathematics, University of Manitoba, Winnipeg, MB, Canada
| | - Liang Chen
- Department of Applied Mathematics, Centre for Theoretical Neuroscience, University of Waterloo, Waterloo, ON, Canada
| | - Wilten Nicola
- Hotchkiss Brain Institute, Cumming School of Medicine, University of Calgary, Calgary, AB, Canada
| | - Sue Ann Campbell
- Department of Applied Mathematics, Centre for Theoretical Neuroscience, University of Waterloo, Waterloo, ON, Canada
| |
Collapse
|
3
|
Protachevicz PR, Iarosz KC, Caldas IL, Antonopoulos CG, Batista AM, Kurths J. Influence of Autapses on Synchronization in Neural Networks With Chemical Synapses. Front Syst Neurosci 2020; 14:604563. [PMID: 33328913 PMCID: PMC7734146 DOI: 10.3389/fnsys.2020.604563] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/09/2020] [Accepted: 11/05/2020] [Indexed: 11/29/2022] Open
Abstract
A great deal of research has been devoted on the investigation of neural dynamics in various network topologies. However, only a few studies have focused on the influence of autapses, synapses from a neuron onto itself via closed loops, on neural synchronization. Here, we build a random network with adaptive exponential integrate-and-fire neurons coupled with chemical synapses, equipped with autapses, to study the effect of the latter on synchronous behavior. We consider time delay in the conductance of the pre-synaptic neuron for excitatory and inhibitory connections. Interestingly, in neural networks consisting of both excitatory and inhibitory neurons, we uncover that synchronous behavior depends on their synapse type. Our results provide evidence on the synchronous and desynchronous activities that emerge in random neural networks with chemical, inhibitory and excitatory synapses where neurons are equipped with autapses.
Collapse
Affiliation(s)
| | - Kelly C Iarosz
- Faculdade de Telêmaco Borba, FATEB, Telêmaco Borba, Brazil.,Graduate Program in Chemical Engineering, Federal University of Technology Paraná, Ponta Grossa, Brazil
| | - Iberê L Caldas
- Institute of Physics, University of São Paulo, São Paulo, Brazil
| | - Chris G Antonopoulos
- Department of Mathematical Sciences, University of Essex, Colchester, United Kingdom
| | - Antonio M Batista
- Institute of Physics, University of São Paulo, São Paulo, Brazil.,Department of Mathematics and Statistics, State University of Ponta Grossa, Ponta Grossa, Brazil
| | - Jurgen Kurths
- Department Complexity Science, Potsdam Institute for Climate Impact Research, Potsdam, Germany.,Department of Physics, Humboldt University, Berlin, Germany.,Centre for Analysis of Complex Systems, Sechenov First Moscow State Medical University, Moscow, Russia
| |
Collapse
|
4
|
Nair N, Bochove E, Braiman Y. Phase-locking of arrays of weakly coupled semiconductor lasers. OPTICS EXPRESS 2018; 26:20040-20050. [PMID: 30119320 DOI: 10.1364/oe.26.020040] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2018] [Accepted: 07/14/2018] [Indexed: 06/08/2023]
Abstract
In this paper we study the conditions for achieving almost perfect phase locking in large arrays of semiconductor diodes. We show that decayed non-local coupling of diode lasers can provide the necessary conditions for robust phase synchronization of an entire diode laser array. Perfect global coupling is known to allow for robust synchronization, however it is often physically impossible or impractical to achieve. We show that when diodes are coupled via the decayed non-local coupling layout, the dominant transverse mode of the laser array has a uniform phase across the lasers and can be stable. This state is robust to noise and frequency disorder and can be realized under periodic (fixed-intensity limit cycle) continuous-wave and chaotic behavior of lasers.
Collapse
|
5
|
Hart JD, Pade JP, Pereira T, Murphy TE, Roy R. Adding connections can hinder network synchronization of time-delayed oscillators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:022804. [PMID: 26382451 DOI: 10.1103/physreve.92.022804] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2015] [Indexed: 06/05/2023]
Abstract
We provide experimental evidence that adding links to a network's structure can hinder synchronization. Our experiments and theoretical analysis of networks of time-delayed optoelectronic oscillators uncover the scenario of loss of identical synchronization upon connectivity modifications. This counterintuitive loss of synchronization can occur even when the network structure is improved from a connectivity perspective. Utilizing a master stability function approach, we show that a time delay in the coupling of nodes plays a crucial role in determining a network's synchronization properties and that this effect is more prominent in directed networks than in undirected networks, especially for large networks. Our results provide insight into the impact of structural modifications in networks with equal coupling delays and open the path to design changes to the network connectivity to sustain and control the performance of real-world networks.
Collapse
Affiliation(s)
- Joseph D Hart
- Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA
- Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Jan Philipp Pade
- Institude of Mathematics, Humboldt University of Berlin, Unter der Linden 6, 10099 Berlin, Germany
| | - Tiago Pereira
- Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
- Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, 13560-970 São Carlos, São Paulo, Brazil
| | - Thomas E Murphy
- Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA
- Department of Electrical and Computer Engineering, University of Maryland, College Park, Maryland 20742, USA
| | - Rajarshi Roy
- Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA
- Department of Physics, University of Maryland, College Park, Maryland 20742, USA
- Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
| |
Collapse
|