Grazing bifurcations in impact oscillators characterize the transition in asymptotic dynamics between impacting and non-impacting motions. Several different grazing bifurcation scenarios under variations of a single system parameter have been previously documented in the literature. In the present paper, the transition between two characteristically different co-dimension-one grazing bifurcatio...

This paper presents a theory for characterization of the blowout bifurcation by periodic orbits. Blowout bifurcation in chaotic systems occurs when a chaotic attractor, lying in some symmetric invariant subspace, becomes transversely unstable. We present an analysis and numerical results that indicate that the bifurcation is mediated by changes in the transverse stability of an infinite number ...

This paper provides a global picture of the bifurcation scenario of the Hindmarsh-Rose model. A combination between simulations and numerical continuations is used to unfold the complex bifurcation structure. The bifurcation analysis is carried out by varying two bifurcation parameters and evidence is given that the structure that is found is universal and appears for all combinations of bifurc...

In this paper, motivated by the interest and relevance of the study of tumor growth models, a central point of our investigation is the study of the chaotic dynamics and the bifurcation structure of Weibull-Gompertz-Fréchet’s functions: a class of continuousdefined one-dimensional maps. Using symbolic dynamics techniques and iteration theory, we established that depending on the properties of t...

the carotid sinus is a modification in the vascular wall near the bifurcation each common carotid artery and acts as baroreceptor. in this study 16 adult and apparently healthy buffaloes ie. 8 male and 8 female used for the as well as macroscopic orientation microscopic study of the carotid sinus. our study revealed that in the buffalo, carotid sinus is a dilatation in common carotid artery at ...

We consider a basic rate-equation model for the gains and intensities of two identical lasers that are mutually coupled via fast saturable absorbers. A numerical bifurcation study with the package AUTO reveals a considerable amount of multistability between different types of stable solutions of the system, which include stationary states, as as well as in-phase, anti-phase and intermediate-pha...

We show that incorporating spatial dispersal of individuals into a simple vaccination epidemic model may give rise to a model that exhibits rich dynamical behavior. Using an SIVS (susceptible – infected – vaccinated – susceptible) model as a basis, we describe the spread of an infectious disease in a population split into two regions. In each sub-population, both forward and backward bifurcatio...

In this paper, we focus on a ratio dependent predator–prey system with selfand cross-diffusion and constant harvesting rate. By making use of a brief stability and bifurcation analysis, we derive the symbolic conditions for Hopf, Turing and wave bifurcations of the system in a spatial domain. Additionally, we illustrate spatial pattern formations caused by these bifurcations via numerical examp...

is a model validated previously. In our study, only the average queue size k q − is considered, and the results are based on analytical model rather than actual measurements. The instabilities in the model are studied numerically using the conventional nonlinear bifurcation analysis. Extending from this bifurcation analysis, a modified RED algorithm is derived to prevent the observed bifurcatio...

We perform bifurcation analysis of plane wave solutions in a one-dimensional complex cubic-quintic Ginzburg–Landau equation with delayed feedback. Our study reveals how multistability and snaking behavior of plane waves emerge as time delay is introduced. For intermediate values of the delay, bifurcation diagrams are obtained by a combination of analytical and numerical methods. For large delay...