Topic
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: The main finding is that, unlike Replicator Dynamics, generic Hopf bifurcation and thus, stable limit cycles, occur under the Logit Dynamics, even for three-strategy games.
42 citations
TL;DR: In this article, a four-dimensional four-parameter Chua model with cubic nonlinearity was studied applying numerical continuation and numerical solutions methods, and the bifurcation curves of the model were obtained with the possibility to describe the shrimp-shaped domains and their endoskeletons.
42 citations
TL;DR: In this paper, a simplified model of a container crane subject to delayed feedback is investigated and conditions for a Hopf bifurcation to stable/unstable limit-cycle solutions are determined.
Abstract: A simplified model of a container crane subject to a delayed feedback is investigated. The conditions for a Hopf bifurcation to stable/unstable limit-cycle solutions are determined. It is shown that a subcritical Hopf bifurcation to unstable oscillations cannot be ruled out and the undesired coexistence of stable large amplitude oscillations and a stable equilibrium endangers the robustness of time-delay control strategies. The bifurcation is analyzed both analytically and numerically using a continuation method.
42 citations
TL;DR: In this paper, a delay-differential system for modeling an artificial neural network with two neurons is investigated and linear stability and Hopf bifurcation including its direction and stability of the network with four delays are established.
Abstract: A delay-differential system modelling an artificial neural network with two neurons is investigated. At appropriate parameter values, linear stability and Hopf bifurcation including its direction and stability of the network with four delays are established in this paper. The main tools to obtain our results are the normal form method and the center manifold theory introduced by Hassard. Simulations show that the theoretically predicted values are in excellent agreement with the numerically observed behavior. Our results extend and complement some earlier publications.
42 citations
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01 Jan 2001
TL;DR: The main goal of these notes is to describe the combinatorial structure of the Stokes sets for polynomials in one variable, a certain bifurcation diagram in the space of monic polynomial of given degree.
Abstract: The main goal of these notes is to describe the combinatorial structure of the Stokes sets for polynomials in one variable, a certain bifurcation diagram in the space of monic polynomials of given degree (the precise definition is given in section 5). As it turns out, their structure is intimately connected to other bifurcation diagrams (of quadratic differentials, or of Smale functions), and to various combinatorial structures, most prominent among them being Stasheff polyhedra. These notes are expository with proofs at best sketched. A detailed exposition will appear elsewhere.
42 citations