Results 11 to 20 of about 3,779 (211)
International Journal of Mechanical System Dynamics, 2023 Environmental noise can lead to complex stochastic dynamical behaviors in nonlinear systems. In this paper, a Lorenz system with the parameter region with two stable fixed points and a chaotic saddle subject to white Gaussian noise is investigated as an ...
Yong Huang
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Heteroclinic and Periodic Cycles in a Perturbed Convection Model
Journal of Differential Equations, 2002 The authors study a singular perturbation of a system investigated by \textit{J. Guckenheimer} and \textit{P. Holmes} [Math. Proc. Camb. Philos. Soc. 103, No. 1, 189-192 (1988; Zbl 0645.58022)]. They apply a new type of Melnikov function to prove the existence of singular heteroclinic solutions.
Ignacio B. Vivancos, Xiao-Biao Lin
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Stable heteroclinic cycles and symbolic dynamics [PDF]
Chaos: An Interdisciplinary Journal of Nonlinear Science, 1994 Let S10, S11,...,S1n−1 be n circles. A rotation in n circles is a map f:∪i=0n−1S1i→∪ i=0n−1S1i which maps each circle onto another by a rotation. This particular type of interval exchange map arises naturally in bifurcation theory. In this paper we give a full description of the symbolic dynamics associated to such maps.
Alsedà i Soler, Lluís +2 more
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Bifurcations of a Pair of Nonorientable Heteroclinic Cycles
Journal of Mathematical Analysis and Applications, 1998 The authors study some bifurcation problems of a pair of nonorientable heteroclinic cycles of vector fields, which are related to the study of Lorenz equations. The presence of both nonorientable cycles provides \(\Omega\)-explosion. The authors analyze what kinds of bifurcation behaviour happen for a generic two-parameter unfolding of a system with a ...
Jing Zhujun, Qi Dongwen
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Heteroclinic cycles between unstable attractors [PDF]
Nonlinearity, 2008 We consider networks of pulse coupled linear oscillators with non-zero delay where the coupling between the oscillators is given by the Mirollo-Strogatz function. We prove the existence of heteroclinic cycles between unstable attractors for a network of four oscillators and for an open set of parameter values.
Easwar Subramanian +2 more
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High frequency forcing of an attracting heteroclinic cycle
Portugaliae Mathematica, 2023 This article is concerned with the effect of time-periodic forcing on a vector field exhibiting an attracting heteroclinic network. We show that as the forcing frequency tends to infinity, the dynamics reduces to that of a network under constant forcing, the constant being the average value of the forcing term.
Isabel S. Labouriau +1 more
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Transitions of bifurcation diagrams of a forced heteroclinic cycle [PDF]
Journal of Mathematical Analysis and ApplicationsA family of periodic perturbations of an attracting robust heteroclinic cycle defined on the two-sphere is studied by reducing the analysis to that of a one-parameter family of maps on a circle. The set of zeros of the family forms a bifurcation diagram on the cylinder. The different bifurcation diagrams and the transitions between them are obtained as
Isabel S. Labouriau +1 more
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Moduli of stability for heteroclinic cycles of periodic solutions
Discrete & Continuous Dynamical Systems - A, 2019 23 pages, 6 ...
Maria Pires de Carvalho +2 more
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Heteroclinic cycling and extinction in May-Leonard models with demographic stochasticity. [PDF]
J Math Biol, 2023 Barendregt NW, Thomas PJ.
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A theoretical and computational study of heteroclinic cycles in Lotka-Volterra systems. [PDF]
J Math BiolBortolan MC +3 more
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