The transmission of infectious diseases has been studied by mathematical methods since 1760s, among which SIR model shows its advantage in its epidemiological description of spread mechanisms. Here we established a modified SIR model with nonlinear incidence and recovery rates, to understand the influence by any government intervention and hospitalization condition variation in the spread of di...

We consider a predator-prey system with nonmonotonic functional response: p(x) = mx ax2+bx+1 . By allowing b to be negative (b > −2 √ a), p(x) is concave up for small values of x > 0 as it is for the sigmoidal functional response. We show that in this case there exists a Bogdanov–Takens bifurcation point of codimension 3, which acts as an organizing center for the system. We study the Hopf and ...

Quantitative aspects of models describing the dynamics of biological phenomena have been mostly restricted to results of numerical simulations, often by employing standard numerical methods. However, several studies have shown that these methods may fail to reproduce the actual dynamical behavior of the underlying continuous model when the integration time-step, model parameters, or initial con...

We consider examples of loss of stability of chaotic attractors in invariant subspaces (blowouts) that occur on varying two parameters, i.e. codimension two blowout bifurca-tions. Such bifurcations act as organising centres for nearby codimension one behaviour, analogous to the case for codimension two bifurcations of equilibria. We consider examples of blowout bifurcations showing change of cr...

We describe a Sil'nikov-Saddle-Node interaction in the proximity of a Hopf-Saddle-Node bifurcation both from numerical and theoretical viewpoints, inspired in numerical observations of a 3D model of a laser with injected signal. We describe the interaction near the codimension-2 point using a return map controlled by the parameters of the bifurcation. The theoretical predictions compare well wi...

One of the important medical problems is infectious diseases such as HIV and hepatitis which annually causes the death of many people. So it is important to study infectious diseases parametric models. In this paper, we investigate differential equations system of HIV and hepatitis (with delay and without delay) from the stability and codimension-one bifurcation point of view. We show that thei...

We study a codimension two steady-state/steady-state mode interaction with D4 symmetry, where the center manifold is three-dimensional. Primary branches of equilibria undergo secondary Hopf bifurcations to periodic solutions which undergo further bifurcations leading to chaotic dynamics. This is not an exponentially small effect, and the chaos obtained in simulations using DsTool is large-scale...

The analysis of the Takens-Bogdanov bifurcation of the equilibrium at the origin in the Chua’s equation with a cubic nonlinearity is carried out. The local analysis provides, in first approximation, different bifurcation sets, where the presence of several dynamical behaviours (including periodic, homoclinic and heteroclinic orbits) is predicted. The local results are used as a guide to apply t...

We consider a family of differential equations that describes traveling waves in a reaction diffusion equation modeling oxidation of carbon oxide on a platinum surface, near the onset of spatio-temporal chaos. The organizing bifurcation for the bifurcation structure with small carbon oxide pressures, turns out to be a codimension three bifurcation involving a homoclinic orbit to an equilibrium ...