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Bashkirtseva I, Ryashko L. Chaotic transients, riddled basins, and stochastic transitions in coupled periodic logistic maps. CHAOS (WOODBURY, N.Y.) 2021; 31:053101. [PMID: 34240946 DOI: 10.1063/5.0050613] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2021] [Accepted: 04/12/2021] [Indexed: 06/13/2023]
Abstract
A system of two coupled map-based oscillators is studied. As units, we use identical logistic maps in two-periodic modes. In this system, increasing coupling strength significantly changes deterministic regimes of collective dynamics with coexisting periodic, quasiperiodic, and chaotic attractors. We study how random noise deforms these dynamical regimes in parameter zones of mono- and bistability, causes "order-chaos" transformations, and destroys regimes of in-phase and anti-phase synchronization. In the analytical study of these noise-induced phenomena, a stochastic sensitivity technique and a method of confidence domains for periodic and multi-band chaotic attractors are used. In this analysis, a key role of chaotic transients and geometry of "riddled" basins is revealed.
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Affiliation(s)
- Irina Bashkirtseva
- Department of Theoretical and Mathematical Physics, Ural Federal University, Lenina, 51, 620000 Ekaterinburg, Russia
| | - Lev Ryashko
- Department of Theoretical and Mathematical Physics, Ural Federal University, Lenina, 51, 620000 Ekaterinburg, Russia
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Kanno K, Hida T, Uchida A, Bunsen M. Spontaneous exchange of leader-laggard relationship in mutually coupled synchronized semiconductor lasers. Phys Rev E 2017; 95:052212. [PMID: 28618492 DOI: 10.1103/physreve.95.052212] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2017] [Indexed: 11/07/2022]
Abstract
We investigate the instantaneous behavior of synchronized temporal wave forms in two mutually coupled semiconductor lasers numerically and experimentally. The temporal wave forms of two lasers are synchronized with a propagation delay time, with one laser oscillating in advance of the other, known as the leader-laggard relationship. The leader-laggard relationship can be determined by measuring the cross-correlation between the two temporal wave forms with the propagation delay time. The leader can be identified when the optical carrier frequency of the leader laser is higher than that of the other laser. However, spontaneous exchange between the leader and laggard lasers can be observed in low-frequency fluctuations by short-term cross-correlation measurements, even for a fixed initial optical frequency detuning. The spontaneous exchange of the leader-laggard relationship originates from alternation of partial optical frequency locking between the two lasers. This observation is analyzed using a phase space trajectory on steady-state solutions for mutually coupled lasers with optical frequency detuning.
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Affiliation(s)
- Kazutaka Kanno
- Department of Electronics Engineering and Computer Science, Fukuoka University, 8-19-1 Nanakuma, Johnan-ku, Fukuoka 814-0180, Japan
| | - Takuya Hida
- Department of Information and Computer Sciences, Saitama University, 255 Shimo-okubo, Sakura-ku, Saitama City, Saitama 338-8570, Japan
| | - Atsushi Uchida
- Department of Information and Computer Sciences, Saitama University, 255 Shimo-okubo, Sakura-ku, Saitama City, Saitama 338-8570, Japan
| | - Masatoshi Bunsen
- Department of Electronics Engineering and Computer Science, Fukuoka University, 8-19-1 Nanakuma, Johnan-ku, Fukuoka 814-0180, Japan
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Bayani A, Hadaeghi F, Jafari S, Murray G. Critical slowing down as an early warning of transitions in episodes of bipolar disorder: A simulation study based on a computational model of circadian activity rhythms. Chronobiol Int 2017; 34:235-245. [PMID: 28060532 DOI: 10.1080/07420528.2016.1272608] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Abstract
Bipolar disorder is characterized by repeated episodes of mania and depression, and can be understood as pathological complex system behaviour involving cognitive, affective and psychomotor disturbance. Accurate prediction of episode transitions in the long-term pattern of mood changes in bipolar disorder could improve the management of the disorder by providing an objective early warning of relapse. In particular, circadian activity changes measured via actigraphy may contain clinically relevant signals of imminent systemic dysregulation. In this study, we propose a mathematical index to investigate the correlation between apparently irregular circadian activity rhythms and critical transitions in episodes of bipolar disorder. Not only does the proposed index illuminate the effects of pharmacological and psychological therapies in control over the state, but it also provides a framework to understand the dynamic (or state-dependent) control strategies. Modelling analyses using our new approach suggest that key clinical goals are minimizing side effects of mood stabilizers as well as increasing the efficiency of other therapeutic strategies.
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Affiliation(s)
- Atiyeh Bayani
- a Faculty of Biomedical Engineering , Amirkabir University of Technology , Tehran , Iran
| | - Fatemeh Hadaeghi
- a Faculty of Biomedical Engineering , Amirkabir University of Technology , Tehran , Iran
| | - Sajad Jafari
- a Faculty of Biomedical Engineering , Amirkabir University of Technology , Tehran , Iran
| | - Greg Murray
- b Department of Psychological Sciences, Faculty of Health, Arts and Design , Swinburne University of Technology , Hawthorn , Victoria , Australia
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Karsaklian Dal Bosco A, Akizawa Y, Kanno K, Uchida A, Harayama T, Yoshimura K. Photonic integrated circuits unveil crisis-induced intermittency. OPTICS EXPRESS 2016; 24:22198-22209. [PMID: 27661954 DOI: 10.1364/oe.24.022198] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We experimentally investigate an intermittent route to chaos in a photonic integrated circuit consisting of a semiconductor laser with time-delayed optical feedback from a short external cavity. The transition from a period-doubling dynamics to a fully-developed chaos reveals a stage intermittently exhibiting these two dynamics. We unveil the bifurcation mechanism underlying this route to chaos by using the Lang-Kobayashi model and demonstrate that the process is based on a phenomenon of attractor expansion initiated by a particular distribution of the local Lyapunov exponents. We emphasize on the crucial importance of the distribution of the steady-state solutions introduced by the time-delayed feedback on the existence of this intermittent dynamics.
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Hadaeghi F, Hashemi Golpayegani MR, Murray G. Towards a complex system understanding of bipolar disorder: A map based model of a complex winnerless competition. J Theor Biol 2015; 376:74-81. [PMID: 25728789 DOI: 10.1016/j.jtbi.2015.02.020] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2014] [Revised: 02/06/2015] [Accepted: 02/17/2015] [Indexed: 12/20/2022]
Abstract
Bipolar disorder is characterized by repeated erratic episodes of mania and depression, which can be understood as pathological complex system behavior involving cognitive, affective and psychomotor disturbance. In order to illuminate dynamical aspects of the longitudinal course of the illness, we propose here a novel complex model based on the notion of competition between recurrent maps, which mathematically represent the dynamics of activation in excitatory (Glutamatergic) and inhibitory (GABAergic) pathways. We assume that manic and depressive states can be considered stable sub attractors of a dynamical system through which the mood trajectory moves. The model provides a theoretical framework which can account for a number of complex phenomena of bipolar disorder, including intermittent transition between the two poles of the disorder, rapid and ultra-rapid cycling of episodes and manicogenic effects of antidepressants.
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Affiliation(s)
- Fatemeh Hadaeghi
- Complex Systems and Cybernetics Control Laboratory, Biomedical Engineering Faculty, Amirkabir University of Technology, Tehran, Iran
| | - Mohammad Reza Hashemi Golpayegani
- Complex Systems and Cybernetics Control Laboratory, Biomedical Engineering Faculty, Amirkabir University of Technology, Tehran, Iran.
| | - Greg Murray
- Faculty of Health, Arts and Design, Swinburne University of Technology, Hawthorn, VIC, Australia
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Hadaeghi F, Hashemi Golpayegani MR, Moradi K. Does "crisis-induced intermittency" explain bipolar disorder dynamics? Front Comput Neurosci 2013; 7:116. [PMID: 23986691 PMCID: PMC3750208 DOI: 10.3389/fncom.2013.00116] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2013] [Accepted: 07/29/2013] [Indexed: 11/26/2022] Open
Affiliation(s)
- Fatemeh Hadaeghi
- Biomedical Engineering Faculty, Amirkabir University of TechnologyTehran, Iran
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Ibarz B, Tanaka G, Sanjuán MAF, Aihara K. Sensitivity versus resonance in two-dimensional spiking-bursting neuron models. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:041902. [PMID: 17500916 DOI: 10.1103/physreve.75.041902] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2006] [Revised: 12/12/2006] [Indexed: 05/15/2023]
Abstract
Through phase plane analysis of a class of two-dimensional spiking and bursting neuron models, covering some of the most popular map-based neuron models, we show that there exists a trade-off between the sensitivity of the neuron to steady external stimulation and its resonance properties, and how this trade-off may be tuned by the neutral or asymptotic character of the slow variable. Implications of the results for the suprathreshold behavior of the neurons, both by themselves and as part of networks, are presented in different regimes of interest, such as the excitable, regular spiking, and bursting regimes. These results establish a consistent link between single-neuron parameters and resulting network dynamics, and will hopefully be useful as a guide for modeling.
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Affiliation(s)
- Borja Ibarz
- Nonlinear Dynamics and Chaos Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain.
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Zambrano S, Mariño IP, Salvadori F, Meucci R, Sanjuán MAF, Arecchi FT. Phase control of intermittency in dynamical systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:016202. [PMID: 16907172 DOI: 10.1103/physreve.74.016202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2006] [Indexed: 05/11/2023]
Abstract
We present a nonfeedback method to tame or enhance crisis-induced intermittency in dynamical systems. By adding a small harmonic perturbation to a parameter of the system, the intermittent behavior can be suppressed or enhanced depending on the value of the phase difference between the main driving and the perturbation. The validity of the method is shown both in the model and in an experiment with a CO2 laser. An analysis of this scheme applied to the quadratic map near crisis illustrates the role of phase control in nonlinear dynamical systems.
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Affiliation(s)
- Samuel Zambrano
- Nonlinear Dynamics and Chaos Group, Departamento de Ciencias de la Naturaleza y Física Aplicada, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain
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