Oscillation analysis of the solutions for a four coupled FHN network model with delays

Feng, Chunhua; Plamondon, Réjean

doi:10.1109/ijcnn.2014.6889505

Cited by 1 publication

(1 citation statement)

References 14 publications

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“…The stability and oscillation of the solutions is investigated by constructing of Liapunov functional and applying the Chafees limit cycle criterion. Zhen and Xu [42] and also Lin [50] generalized the FHN models to a three coupled FHN neurons and Feng and Plamondon [51] to a four coupled FHN neurons with time delay. They derived some criteria to determine the periodic oscillation were provided in the multiple delayed FHN neural system with nonidentical cells.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation structure of two coupled FHN neurons with delay

Tehrani

Razvan

2015

Mathematical Biosciences

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This paper presents an investigation of the dynamics of two coupled non-identical FitzHugh-Nagumo neurons with delayed synaptic connection. We consider coupling strength and time delay as bifurcation parameters, and try to classify all possible dynamics which is fairly rich. The neural system exhibits a unique rest point or three ones for the different values of coupling strength by employing the pitchfork bifurcation of non-trivial rest point. The asymptotic stability and possible Hopf bifurcations of the trivial rest point are studied by analyzing the corresponding characteristic equation. Homoclinic, fold, and pitchfork bifurcations of limit cycles are found. The delay-dependent stability regions are illustrated in the parameter plane, through which the double-Hopf bifurcation points can be obtained from the intersection points of two branches of Hopf bifurcation. The dynamical behavior of the system may exhibit one, two, or three different periodic solutions due to pitchfork cycle and torus bifurcations (Neimark-Sacker bifurcation in the Poincare map of a limit cycle), of which detection was impossible without exact and systematic dynamical study. In addition, Hopf, double-Hopf, and torus bifurcations of the non trivial rest points are found. Bifurcation diagrams are obtained numerically or analytically from the mathematical model and the parameter regions of different behaviors are clarified.

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Section: Introductionmentioning

confidence: 99%