Global bifurcations and chaos
WebJan 1, 1995 · Abstract. Bifurcation and Chaos presents a collection of especially written articles describing the theory and application of nonlinear dynamics to a wide variety of problems encountered in ... WebAug 1, 2010 · Global bifurcations are catastrophic and always lead to the merging or disappearance of attractors. A list of global bifurcation types is compared to a list of ecological consequences of occurring global bifurcations. ... Global Bifurcations and Chaos: Analytical methods (1988) S. Wiggins Introduction to Applied Nonlinear …
Global bifurcations and chaos
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WebJul 28, 2024 · We present a detailed numerical case study of how global stable and unstable manifolds of the saddle equilibrium and of bifurcating periodic orbits interact … WebFeb 16, 2024 · Layek, An Introduction to Dynamical Systems and Chaos (Springer, 2015). ... Global bifurcations are observed mainly when invariant structures collide with each other like invariant manifold and chaotic attractors, yielding to the destruction of the chaotic attractor. In this scenario, the destruction causes a considerable modification of the ...
WebMay 31, 2013 · In this paper, global bifurcations and chaotic dynamics under bounded noise perturbation for the nonlinear normalized radial electric field near plasma are investigated using the Melnikov method. From this analysis, we get criteria that could be useful for designing the model parameters so that the appearance of chaos could be … WebGlobal bifurcations of cycles: saddle-node infinite period, and homoclinic bifurcations, examples in Josephson Junction and driven pendulum in 2D (St §8.4 and§ 8.5) Quasi periodicity, coupled oscillators, nonlinear resonance/ frequency locking (Frequency locking of glacial cycles to earth orbital variations), (St §8.6)
WebGlobal Bifurcations and Chaos: Analytical Methods is unique in the literature of chaos in that it not only defines the concept of chaos in deterministic systems, but it describes the … WebDec 1, 2010 · Communications in Nonlinear Science and Numerical Simulation. Volume 15, Issue 12, December 2010, Pages 4007-4019, December 2010, Pages 4007-4019
WebA period-doubling cascade is an infinite sequence of period-doubling bifurcations. Such cascades are a common route by which dynamical systems develop chaos. In hydrodynamics, they are one of the possible routes to turbulence. Period-halving bifurcations (L) leading to order, followed by period-doubling bifurcations (R) leading …
WebJun 30, 2006 · The cell mapping methods are presented for global bifurcations in stochastic and deterministic, nonlinear dynamical systems in the third chapter. The fourth … symons creek ncWebNov 16, 2024 · Abstract. In this paper, local dynamics, bifurcations and chaos control in a discrete-time predator-prey model have been explored in . It is proved that the model has a trivial fixed point for all parametric values and the unique positive fixed point under definite parametric conditions. thaddeus jimenez caseWebMar 1, 2024 · Attractors, Bifurcations, & Chaos - now in its second edition - begins with an introduction to mathematical methods in modern nonlinear dynamics and deals with differential equations. Phenomena such as bifurcations and deterministic chaos are given considerable emphasis, both in the methodological part, and in the second part, … symons creek tabernacleWebJul 27, 2024 · Homoclinic bifurcations are important phenomena that cause global rearrangements of the dynamics in phase space, including changes to basins of attractions and the generation of chaotic dynamics. symons cookoutWebcycle attractors in map (1). Bischi and Kopel [4] used the method of critical curves to analyze the global bifurcations and illustrate the qualitative changes in the topological structure of the basins of Kopel’s model. Anderson et al. [3] considered the basins of attraction in the case of three nontrivial Nash equilibria in Kopel’s map and found that a circle, lines, and … symons crescent morwellWebMay 1, 2024 · Nature of the bifurcations is determined using normal-form reduction. Another important contribution is to unveil the occurrence of delay-induced subcritical and supercritical, non-degenerate and degenerate Hopf bifurcations around the coexisting steady state. ... Dubey B., Sajan A., Kumar A., Stability switching and chaos in a … thaddeus l wilsonWebOct 15, 2024 · In regions where coexisting solutions are found, homoclinic connections ensue codimension-two Bogdanov–Takens and Double-Hopf bifurcations and that for a … symons corn pudding