On a class of non linear differential operators of first order with singular point.
On a codimension three bifurcation
On Chaotic Subthreshold Oscillations in a Simple Neuronal Model
In a simple FitzHugh-Nagumo neuronal model with one fast and two slow variables, a sequence of period-doubling bifurcations for small-scale oscillations precedes the transition into the spiking regime. For a wide range of values of the timescale separation parameter, this scenario is recovered numerically. Its relation to the singularly perturbed integrable system is discussed.
On classical intrinsically resonant formal perturbation theory
On equilibrium bifurcations in the cosymmetry collapse of a dynamical system.
On limit cycles of piecewise differential systems formed by arbitrary linear systems and a class of quadratic systems
We study the continuous and discontinuous planar piecewise differential systems separated by a straight line and formed by an arbitrary linear system and a class of quadratic center. We show that when these piecewise differential systems are continuous, they can have at most one limit cycle. However, when the piecewise differential systems are discontinuous, we show that they can have at most two limit cycles, and that there exist such systems with two limit cycles. Therefore, in particular, we...
On lopsided systems.
On quadratic symplectic mappings.
On some dynamical properties of S-unimodal maps on an interval
On the Bautin bifurcation for systems of delay differential equations.
On the bifurcation set of complex polynomial with isolated singularities at infinity
On the Birkhoff normal form of a completely integrable hamiltonian system near a fixed point with resonance
On the critical periods of Liénard systems with cubic restoring forces.
On the dynamics of a delayed SIR epidemic model with a modified saturated incidence rate.
On the dynamics of polynomial-like mappings
On the existence and stability of unfoldings of equivariant two-parameter bifurcation problems.
On the existence of a periodic solution of a nonlinear ordinary differential equation.
On the existence of bright solitons in cubic-quintic nonlinear Schrödinger equation with inhomogeneous nonlinearity.
On the existence of chaotic behaviour of diffeomorphisms
For several specific mappings we show their chaotic behaviour by detecting the existence of their transversal homoclinic points. Our approach has an analytical feature based on the method of Lyapunov-Schmidt.
On the existence of homoclinic points