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: In this paper, a new method for distinguishing chaotic, periodic and quasi-periodic orbits and analysis the Hopf bifurcation using an analytic technique for the Lu system is introduced.
Abstract: In this paper, we introduce a new practical method for distinguishing the chaotic, periodic and quasi-periodic orbits, and analysis the Hopf bifurcation using an analytic technique for the Lu system. As a result, we have further explored the dynamical behaviors.
43 citations
Book•
01 Oct 1993
TL;DR: In this paper, the authors present a monograph for researchers and graduate students in the areas of Hamiltonian systems, singularity theory, and equivariant maps, which will appeal to both researchers and students.
Abstract: The monograph will appeal to researchers and graduate students in the areas of symplectic maps, Hamiltonian systems, singularity theory and equivariant ...
43 citations
TL;DR: For travelling waves, in which release events occur sequentially, the speed of waves is constructed in terms of the time-scale at which pumps operate, which means that the inclusion of calcium pumps leads to multiple solutions.
43 citations
TL;DR: The bifurcation diagram for a vibrofluidized granular gas in N connected compartments is constructed and discussed, in which the uniform distribution becomes unstable and gives way to a clustered state when the driving intensity is decreased.
Abstract: The bifurcation diagram for a vibrofluidized granular gas in N connected compartments is constructed and discussed. At vigorous driving, the uniform distribution ~in which the gas is equi-partitioned over the compartments! is stable. But when the driving intensity is decreased this uniform distribution becomes unstable and gives way to a clustered state. For the simplest case, N52, this transition takes place via a pitchfork bifurcation but for all N.2 the transition involves saddle-node bifurcations. The associated hysteresis becomes more and more pronounced for growing N. In the bifurcation diagram, apart from the uniform and the one-peaked distributions, also a number of multipeaked solutions occur. These are transient states. Their physical relevance is discussed in the context of a stability analysis.
43 citations
TL;DR: Stability analysis shows that the onset of Hopf bifurcation can be delayed or advanced via a PD controller by setting proper control parameters, and theHopf bIfurcation of the model became controllable to achieve desirable behaviors which is applicable in certain circumstances.
43 citations