We consider the singularly perturbed limit of periodically excited two-dimensional FitzHugh-Nagumo systems. We show that the dynamics of such systems are essentially governed by an one-dimensional map and present a numerical scheme to accurately compute it together with its Lyapunov exponent. We then investigate the occurrence of chaos by varying the parameters of the system, with especial emphasis on the simplest possible chaotic oscillations. Our results corroborate and complement some recent works on bifurcations and routes to chaos in certain particular cases corresponding to piecewise linear FitzHugh-Nagumo-like systems.
We analyze a pair of delay-coupled FitzHugh-Nagumo oscillators exhibiting in-out intermittency as a part of the generating mechanism of extreme events. We study in detail the characteristics of in-out intermittency and identify the invariant subsets involved --- a saddle fixed point and a saddle periodic orbit --- neither of which are chaotic as in the previously reported cases of in-out intermittency. Based on the analysis of a periodic attractor possessing in-out dynamics, we can characterize the approach to the invariant synchronization manifold and the spiralling out to the saddle periodic…
An expression for the group delay of the FitzHugh-Nagumo model in response to low amplitude input is obtained by linearisation of the cubic term of the voltage equation around its stable fixed-point. It is found that a negative group delay exists for low frequencies, indicating that the evolution of slowly fluctuating signals are anticipated by the voltage dynamics. The effects of the group delay for different types of signals are shown numerically for the non-linearised FitzHugh-Nagumo model, and some observations on the signal aspects that are anticipated are stated.
The asymptotic limit-cycle analysis of the FitzHugh-Nagumo equations is presented. In this work, we obtain an explicit analytical expression for the relaxation-oscillation period that is accurate within 1\% of their numerical values. In addition, we derive the critical parametric values leading to canard explosions and implosions in its associated limit cycles.
Modulation of Neuronal Firing Modes by Electric Fields in a Thermosensitive FitzHugh-Nagumo Model
E. L. F. Nguessap, A.C. Roque, F.F. Ferreira Department of Physics,FFCLRP-University of Sao Paulo, 14040900, Ribeirao Preto-SP, Brazil Corresponding author
Hopf bifurcation and stochastic spiking in an antiferromagnetic FitzHugh--Nagumo normal form
Doctoral School at the University of Rzeszów（热舒夫大学博士学院）；Institute of Physics, Faculty of Exact and Technical Sciences, University of Rzeszów（热舒夫大学精确与技术科学学院物理研究所）；Department of Physics, Indian Institute of Technology (Banaras Hindu University)（印度理工学院（贝拿勒斯印度教大学）物理系）；Department of Physics and Medical Engineering, Rzeszów University of Technology（热舒夫理工大学物理与医学工程系）
The three-dimensional (3D) Fitzhugh-Nagumo neuron model with inertia was shown to exhibit a chaotic mixed-mode dynamics composed of large-amplitude spikes separated by an irregular number of small-amplitude chaotic oscillations. In contrast to the standard 2D Fitzhugh-Nagumo model driven by noise, the interspike-intervals distribution displays a complex arrangement of sharp peaks related to the unstable periodic orbits of the chaotic attractor. For many ranges of parameters controlling the excitability of the system, we observe that chaotic mixed-mode states consist of lapses of nearly regular…
In a previous paper we have proposed a new method for proving the existence of "canard solutions" for three and four-dimensional singularly perturbed systems with only one fast variable which improves the methods used until now. The aim of this work is to extend this method to the case of four-dimensional singularly perturbed systems with two slow and two fast variables. This method enables to state a unique generic condition for the existence of "canard solutions" for such four-dimensional singularly perturbed systems which is based on the stability of folded singularities (pseudo singular po…
In this paper, we study the impact of electrical and memristor-based couplings on some neuron-like spiking regimes, previously observed in the ensemble of two identical FitzHugh-Nagumo elements with chemical excitatory coupling. We demonstrate how increasing strength of these couplings affects on such stable periodic regimes as spiking in-phase, anti-phase and sequential activity. We show that the presence of electrical and memristor-based coupling does not essentially affect regimes of in-phase activity. Such regimes do not changes remaining stable ones. However, it is not the case for regime…
Adaptive transitions in FitzHugh-Nagumo networks with Hebb-Oja coupling rules
National Center for Scientific Research “Demokritos”（德谟克利特国家科学研究中心）；Democritus University of Thrace（色雷斯德谟克利特大学）；Foundation for Research and Technology-Hellas（希腊研究与技术基金会）
