I investigate various instances of bifurcation in a random stationary environment. This is done for a model equation, with a bifurcation parameter fluctuating in

‎In this paper‎, ‎first we discuss a local stability analysis of model was introduced by P‎. ‎J‎. ‎Mumby et‎. ‎al‎. ‎(2007)‎, ‎with $frac{gM^{2}}{M+T}$ as the functional response term‎. ‎We conclude that the grazing intensity is the important parameter to control the existence or extinction of the coral reef‎. ‎Next‎, ‎we consider this model under the influence of the time delay as the bifurcat...

We discuss one parameter families of unimodal maps, with negative Schwarzian derivative, unfolding a saddle-node bifurcation. It was previously shown that for a parameter set of positive Lebesgue density at the bifurcation, the maps possess attracting periodic orbits of high period. We show that there is also a parameter set of positive density at the bifurcation, for which the maps exhibit abs...

Grandmont (1985) found that the parameter space of even the simplest, most classical models is stratified into bifurcation regions. But in such classical models all policies are Ricardian equivalent and all solutions are Pareto optimal. As a result he was not able to reach conclusions about policy relevance of his dramatic discovery. Barnett and He (1999,2002) subsequently found transcritical, ...

We report the bursting in a globally coupled network of mixed population of Active and inactive Josephson junctions. We find the parameter space the parameter regime of the junction where its dynamics is governed by the saddle-node on invariant circle (SNIC) bifurcation. We check the parameter regime where the dynamics of the junction governed by the saddle-node on invariant circle (SNIC) bifur...

We construct a series of n-unimodal approximations to maps of the Hénon type and utilize the associated symbolic dynamics to describe the possible bifurcation structures for such maps. We construct the bifurcation surfaces of the short periodic orbits in the topological parameter space and check numerically that the Hénon map parameter plane (a, b) is topologically equivalent to a two-dimension...

Unlike classical bifurcations, border-collision bifurcations occur when, for example, a fixed point of a continuous, piecewise C1 map crosses a boundary in state space. Although classical bifurcations have been much studied, border-collision bifurcations are not well understood. This paper considers a particular class of border-collision bifurcations, i.e., border-collision period-doubling bifu...

We consider a simple model of an autocatalytic chemical reaction where a limit cycle rapidly increases to infinite period and amplitude, and disappears under variation of a parameter. We show that this bifurcation can be understood from seeing the system as a singular perturbation problem, and we find the bifurcation point by an asymptotic analysis. Scaling laws for period and amplitude are der...

This study provides some connections between bifurcations of onecomplex-parameter complex analytic families of maps of the complex plane C and bifurcations of more general two-real-parameter families of real analytic (or C or C∞) maps of the real plane R. We perform a numerical study of local bifurcations in the families of maps of the plane given by z 7→ F(C,α)(z, z) = z 2 + C + αz where z is ...