3 research outputs found
Numerical bifurcation analysis of two coupled FitzHugh-Nagumo oscillators
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.Comment: 9 pages and 8 figure