In this paper, a three dimensional mathematical model for HTLV-1infection with intracellular delay and immune activation delay is investigated.By applying the frequency domain approach, we show that time delays candestabilize the HAM/TSP equilibrium, leading to Hopf bifurcations and sta-ble or unstable periodic oscillations. At the end, numerical simulations areillustrated.

In this paper, we consider a two-dimensional delay differential system with two delays. By analyzing the distribution of eigenvalues, linear stability of the equilibria and existence of Hopf, Bautin, and Hopf–Hopf bifurcations are obtained in which the time delays are used as the bifurcation parameter. General formula for the direction, period, and stability of the bifurcated periodic solutions...

Systems of coupled oscillators are widely used as models for biological rhythmic oscillations such as human circadian rhythms[1, 2], finger movements, animal locomotion[3], swarms of fireflies that flash in synchrony, synchronous firing of cardiac pacemaker cells[5, 6], and so on. Using these coupled oscillator models, many investigators have studied the mechanism of generation of synchronous o...

This paper is devoted to the analysis of bifurcations in a three-parameter unfolding of a linear degeneracy corresponding to a triple-zero eigenvalue. We carry out the study of codimensiontwo local bifurcations of equilibria (Takens–Bogdanov and Hopf-zero) and show that they are nondegenerate. This allows to put in evidence the presence of several kinds of bifurcations of periodic orbits (secon...

In this article, we study the nonlinear dynamics of a quadratic system in the three dimensional space which can be obtained from a scalar third order differential equation. More precisely, we study the stability and bifurcations which occur in a parameter dependent quadratic system in the three dimensional space. We present an analytical study of codimension one, two and three Hopf bifurcations...

We study the phase reduction of two coupled van der Pol oscillators with asymmetric repulsive coupling under an external harmonic force. We show that the system of two phase oscillators undergoes a Hopf bifurcation and possesses multistability on a 2π-periodic phase plane. We describe the bifurcation mechanisms of formation of multistability in the phase-reduced system and show that the Androno...

In this paper, we review some recent results on the nonlinear dynamics of delayed differential equation models describing interaction between tumor cells and effector immune system, in which delays represent times necessary for molecule production, proliferation, differentiation cells, transport, etc. First consider a tumor-immune system model with single delay pres...

We study the interaction of well-separated oscillating localized structures (oscillons). We show that oscillons emit weakly decaying dispersive waves, which lead to the formation of bound states due to harmonic synchronization. We also show that in optical applications the Andronov-Hopf bifurcation of stationary localized structures leads to a drastic increase in their interaction strength.