Topic
Bifurcation diagram
About: Bifurcation diagram is a research topic. Over the lifetime, 8379 publications have been published within this topic receiving 139664 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: The aim is to investigate how the time delay affects the dynamics of the predator-prey system by choosing the delay as a bifurcation parameter, and the local asymptotic stability of the positive equilibrium and existence of local Hopf bIfurcations are analyzed.
51 citations
TL;DR: The qualitative analysis of the proposed 4-D hyperchaotic four-wing system with a saddle–focus equilibrium confirms its complex dynamic behavior, which is studied by using well-known numerical tools of nonlinear theory, such as the bifurcation diagram, Lyapunov exponents, Poincaré maps, and phase portraits.
Abstract: A novel 4-D hyperchaotic four-wing system with a saddle–focus equilibrium is introduced in this brief. The qualitative analysis of the proposed system confirms its complex dynamic behavior, which is studied by using well-known numerical tools of nonlinear theory, such as the bifurcation diagram, Lyapunov exponents, Poincare maps, and phase portraits. Furthermore, the novel hyperchaotic system is experimentally emulated by an electronic circuit, and its dynamic behavior is studied to confirm the feasibility of the theoretical model.
51 citations
TL;DR: In this article, a global analysis of stochastic bifurcation in a special kind of Duffing system, named as Ueda system, subject to a harmonic excitation and in presence of random noise disturbance is studied in detail by the generalized cell mapping method using digraph.
Abstract: A global analysis of stochastic bifurcation in a special kind of Duffing system, named as Ueda system, subject to a harmonic excitation and in presence of random noise disturbance is studied in detail by the generalized cell mapping method using digraph. It is found that for this dissipative system there exists a steady state random cell flow restricted within a pipe-like manifold, the section of which forms one or two stable sets on the Poincare cell map. These stable sets are called stochastic attractors (stochastic nodes), each of which owns its attractive basin. Attractive basins are separated by a stochastic boundary, on which a stochastic saddle is located. Hence, in topological sense stochastic bifurcation can be defined as a sudden change in character of a stochastic attractor when the bifurcation parameter of the system passes through a critical value. Through numerical simulations the evolution of the Poincare cell maps of the random flow against the variation of noise intensity is explored systematically. Our study reveals that as a powerful tool for global analysis, the generalized cell mapping method using digraph is applicable not only to deterministic bifurcation, but also to stochastic bifurcation as well. By this global analysis the mechanism of development, occurrence, and evolution of stochastic bifurcation can be explored clearly and vividly.
51 citations
Book•
31 Jul 2014
51 citations
TL;DR: In this paper, a planar system of differential delay equations modeling neural activity is investigated, and the stationary points and their saddle-node bifurcations are estimated by an analysis of the associated characteristic equation.
51 citations