This study investigates the dynamics of limited homogeneous populations based on Moran-Ricker model with time delay. The delay in density dependence caused preceding generation to consume fewer resources, leading a decrease required resources. Multimodality is evident model. Some insect species can be described by Moran–Ricker Bifurcations associated flipping, doubling, and Neimark–Sacker for c...

This paper studies the, codimension-3, Boundary-Hopf-Fold (BHF) bifurcation of planar Filippov systems. Filippov systems consist of at least one discontinuity boundary locally separating the phase space to disjoint components with different dynamics. Such systems find applications in several fields, for example, mechanical and electrical engineering, and ecology. The BHF bifurcation appears in ...

Boundary equilibria bifurcation (BEB) arises in piecewise-smooth (PWS) systems when an equilibrium collides with a discontinuity set under parameter variation. Singularly perturbed BEB refers to arising singular perturbation problems which limit as some ? 0 PWS undergo BEB. This work completes classification for codimension-1 singularly the plane initiated by present authors [19], using combina...

Robust attracting heteroclinic cycles have been found in many models of dynamics with symmetries. In all previous examples, robust heteroclinic cycles appear between a number of symmetry broken equilibria. In this paper we examine the first example where there are robust attracting heteroclinic cycles that include the origin, ie a point with maximal symmetry. The example we study is for vector ...

A recent result of J. Damon’s [4] relates the Ae-versal unfoldings of a map-germ f with the KD(G)-versal unfoldings of an associated map germ which induces f from a stable map G. We extend this result to the case where the source is a complete intersection with an isolated singularity. In a similar vein, we also relate the bifurcation theoretic versal deformation of a bifurcation problem (map-g...

In this paper, several nonlinear phenomena found in the study of power system networks are described in the context of bifurcation theory. Toward this end, a widely studied 3-bus power system model is considered. The mechanisms leading to static and dynamic bifurcations of equilibria as well as a cascade of period doubling bifurcations of periodic orbits are investigated. It is shown that the c...