To understand joint effects of logistic growth in target cells and intracellular delay on viral dynamics in vivo, we carry out two-parameter bifurcation analysis of an in-host model that describes infections of many viruses including HIV-I, HBV and HTLV-I. The bifurcation parameters are the mitosis rate r of the target cells and an intracellular delay τ in the incidence of viral infection. We d...

A basic food web of 4 species is considered, of which there is a bottom prey X, two competing predators Y,Z on X, and a super predator W only on Y . The main finding is that population chaos does not require the existence of oscillators in any subsystem of the web. This minimum population chaos is demonstrated by increasing the relative reproductive rate of Z alone without alternating any other...

This study investigates a low degree-of-freedom (DoF) mechanical model of shimmying wheels. The model is studied using bifurcation theory and numerical continuation. Self-excited vibrations, that is, stable and unstable periodic motions of the wheel, are detected with the help of Hopf bifurcation calculations. These oscillations are then followed over a large parameter range for different dampi...

We present a bifurcation analysis of electrical alternans in the two-current Mitchell-Schaeffer (MS) cardiac-cell model using the theory of δ-decidability over the reals. Electrical alternans is a phenomenon characterized by a variation in the successive Action Potential Durations (APDs) generated by a single cardiac cell or tissue. Alternans are known to initiate re-entrant waves and are an im...

We study the dynamics of the Forced Logistic Map in the cylinder. We compute a bifurcation diagram in terms of the dynamics of the attracting set. Different properties of the attracting set are considered, as the Lyapunov exponent and, in the case of having a periodic invariant curve, its period and its reducibility. This reveals that the parameter values for which the invariant curve doubles i...

We consider doubly-periodic travelling waves at the surface of an infinitely deep perfect fluid, only subjected to gravity g and resulting from the nonlinear interaction of two simply periodic travelling waves making an angle 2θ between them. Denoting by μ = gL/c the dimensionless bifurcation parameter ( L is the wave length along the direction of the travelling wave and c is the velocity of th...

We herein propose an algorithm for tracking smooth bifurcations of nonlinear systems with interdependent parameters. The approach is based on a complex formulation the well-known harmonic balance method (HBM). Hill’s used to assess stability computed forced response curves, and minimally extended system built allow parametric continuation detected bifurcation points. feasibility coupling HBM-ba...

Abstract. In this paper, we investigated the dynamics of a diffusive delayed predator-prey system with Holling type II functional response and nozero constant prey harvesting on no-flux boundary condition. At first, we obtain the existence and the stability of the equilibria by analyzing the distribution of the roots of associated characteristic equation. Using the time delay as the bifurcation...

The localization of critical parameter sets called bifurcations is often a central task of the analysis of a nonlinear dynamical system. Bifurcations of codimension 1 that can be directly observed in nature and experiments form surfaces in three dimensional parameter spaces. In this paper we propose an algorithm that combines adaptive triangulation with the theory of complex systems to compute ...

We discuss one parameter families of unimodal maps, with negative Schwarzian derivative, unfolding a saddle-node bifurcation. We show that there is a parameter set of positive but not full Lebesgue density at the bifurcation, for which the maps exhibit absolutely continuous invariant measures which are supported on the largest possible interval. We prove that these measures converge weakly to a...