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Bifurcation diagram

About: Bifurcation diagram is a research topic. Over the lifetime, 8379 publications have been published within this topic receiving 139664 citations.


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TL;DR: In this paper, a ratio dependent predator-prey system with time delay was considered, where the dynamics was logistic with the carrying capacity proportional to the prey population, and the stability and Hopf bifurcation of the system based on the normal form approach and the center manifold theory was analyzed.
Abstract: In this paper, we consider a ratio dependent predator–prey system with time delay where the dynamics is logistic with the carrying capacity proportional to prey population. By considering the time delay as bifurcation parameter, we analyze the stability and the Hopf bifurcation of the system based on the normal form approach and the center manifold theory. Finally, we illustrate our theoretical results by numerical simulations.

41 citations

Journal ArticleDOI
TL;DR: In this article, it is shown that multiple limit cycles, hysteresis loops and catastrophic transitions may possibly accompany a Hopf bifurcation, and the theoretical argument is illustrated in Foley's liquidity cost-business cycle model.

41 citations

Journal ArticleDOI
TL;DR: In this article, the authors consider 2D flows with a homoclinic figure-eight to a dissipative saddle and derive the bifurcation diagram using topological techniques.
Abstract: We consider 2D flows with a homoclinic figure-eight to a dissipative saddle. We study the rich dynamics that such a system exhibits under a periodic forcing. First, we derive the bifurcation diagram using topological techniques. In particular, there is a homoclinic zone in the parameter space with a non-smooth boundary. We provide a complete explanation of this phenomenon relating it to primary quadratic homoclinic tangency curves which end up at some cubic tangency (cusp) points. We also describe the possible attractors that exist (and may coexist) in the system. A main goal of this work is to show how the previous qualitative description can be complemented with quantitative global information. To this end, we introduce a return map model which can be seen as the simplest one which is 'universal' in some sense. We carry out several numerical experiments on the model, to check that all the objects predicted to exist by the theory are found in the model, and also to investigate new properties of the system.

41 citations

Journal ArticleDOI
TL;DR: A new fractionalized logistic map is proposed based on the numerical algorithm of fractional differentiation definition that holds rich dynamical behaviors because of its memory effect and new types of behaviors of bifurcation and chaos are found.

41 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023122
2022326
2021187
2020195
2019166
2018220