Topic
Infinite-period bifurcation
About: Infinite-period bifurcation is a research topic. Over the lifetime, 1113 publications have been published within this topic receiving 19937 citations.
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TL;DR: In this article, the global dynamics of an epidemic model with vital dynamics and nonlinear incidence rate of saturated mass action was studied and it was shown that either the number of infective individuals tends to zero as time evolves or there is a region such that the disease will be persistent if the initial position lies in the region and the disease would disappear if the starting position lies outside this region.
524 citations
TL;DR: A predator-prey system with nonmonotonic functional response is considered and global qualitative and bifurcation analyses are combined to determine the global dynamics of the model.
Abstract: A predator-prey system with nonmonotonic functional response is considered. Global qualitative and bifurcation analyses are combined to determine the global dynamics of the model. The bifurcation a...
458 citations
TL;DR: In this article, the authors consider a two-parameter family of maps of the plane to itself, where each map has a fixed point in the first quadrant and is a diffeomorphism in a neighborhood of this point.
Abstract: We consider a two-parameter family of maps of the plane to itself. Each map has a fixed point in the first quadrant and is a diffeomorphism in a neighborhood of this point. For certain parameter values there is a Hopf bifurcation to an invariant circle, which is smooth for parameter values in a neighborhood of the bifurcation point. However, computer simulations show that the corresponding invariant set fails to be even topologically a circle for parameter values far from the bifurcation point. This paper is an attempt to elucidate some of the mechanisms involved in this loss of smoothness and alteration of topological type.
365 citations
TL;DR: BIFurcation control deals with modification of bifurcation characteristics of a parameterized nonlinear system by a designed control input.
Abstract: Bifurcation control deals with modification of bifurcation characteristics of a parameterized nonlinear system by a designed control input. Typical bifurcation control objectives include delaying t...
350 citations
TL;DR: In this article, the authors investigated Hopf-like bifurcation phenomena and chaotic behavior in cellular neural networks and found that the chaotic attractor found here has properties similar to the famous double scroll attractor.
Abstract: Bifurcation phenomena and chaotic behavior in cellular neural networks are investigated. In a two-cell autonomous system, Hopf-like bifurcation has been found, at which the flow around the origin, an equilibrium point of the system, changes from asymptotically stable to periodic. As the parameter grows further, by reaching another bifurcation value, the generated limit cycle disappears and the network becomes convergent again. Chaos is also presented in a three-cell autonomous system. It is shown that the chaotic attractor found here has properties similar to the famous double scroll attractor. >
277 citations