0000000001019244
AUTHOR
A. S. Tchakoutio Nguetcho
Bifurcations of phase portraits of a Singular Nonlinear Equation of the Second Class
Abstract The soliton dynamics is studied using the Frenkel Kontorova (FK) model with non-convex interparticle interactions immersed in a parameterized on-site substrate potential. The case of a deformable substrate potential allows theoretical adaptation of the model to various physical situations. Non-convex interactions in lattice systems lead to a number of interesting phenomena that cannot be produced with linear coupling alone. In the continuum limit for such a model, the particles are governed by a Singular Nonlinear Equation of the Second Class. The dynamical behavior of traveling wave solutions is studied by using the theory of bifurcations of dynamical systems. Under different para…
Active spike transmission in the neuron model with a winding threshold manifold
International audience; We analyze spiking responses of excitable neuron model with a winding threshold manifold on a pulse stimulation. The model is stimulated with external pulse stimuli and can generate nonlinear integrate-and-fire and resonant responses typical for excitable neuronal cells (all-or-none). In addition we show that for certain parameter range there is a possibility to trigger a spiking sequence with a finite number of spikes (a spiking message) in the response on a short stimulus pulse. So active transformation of N incoming pulses to M (with M>N) outgoing spikes is possible. At the level of single neuron computations such property can provide an active "spike source" comp…
Active spike responses of analog electrical neuron: Theory and experiments
Using an analog electrical FitzHugh-Nagumo neuron including complex threshold excitation (CTE) properties, we analyze its spiking responses under pulse stimulation corresponding to oscillating threshold manifold. The system is subjected to outside pulse stimulus and can generate nonlinear integrate-and-flre and resonant responses which are typical for excitable neuronal cells ("all-or-none"). The answer of the neuron strongly depends on the number and the characteristics of incoming impulses (amplitude, width, strength and frequency). For certain parameters range, there is a possibility to trigger a spiking sequence with a finite number of spikes in response of a single short stimulus pulse…