The behavior of neurons can be modeled by the FitzHugh-Nagumo oscillator model, consisting of two nonlinear differential equations, which simulates the behavior of nerve impulse conduction through the neuronal membrane. In this work, we numerically study the dynamical behavior of two coupled FitzHugh-Nagumo oscillators. We consider unidirectional and bidirectional couplings, for which Lyapunov and isoperiodic diagrams were constructed calculating the Lyapunov exponents and the number of the local maxima of a variable in one period interval of the time-series, respectively. By numerical continuation method the bifurcation curves are also obtained for both couplings. The dynamics of the networks here investigated are presented in terms of the variation between the coupling strength of the oscillators and other parameters of the system. For the network of two oscillators unidirectionally coupled, the results show the existence of Arnold tongues, self-organized sequentially in a branch of a Stern-Brocot tree and by the bifurcation curves it became evident the connection between these Arnold tongues with other periodic structures in Lyapunov diagrams. That system also present multistability shown in the planes of the basin of attractions.
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）
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）
