Results 41 to 50 of about 3,779 (211)
New approach to study the van der Pol equation for large damping
Electronic Journal of Qualitative Theory of Differential Equations, 2018 We present a new approach to establish the existence of a unique limit cycle for the van der Pol equation in case of large damping. It is connected with the bifurcation of a stable hyperbolic limit cycle from a closed curve composed of two heteroclinic ...
Klaus Schneider
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Stability of quasi-simple heteroclinic cycles [PDF]
Dynamical Systems, 2018 The stability of heteroclinic cycles may be obtained from the value of the local stability index along each connection of the cycle. We establish a way of calculating the local stability index for quasi-simple cycles: cycles whose connections are 1-dimensional and contained in flow-invariant spaces of equal dimension.
Sofia B. S. D. Castro +1 more
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Slow Switching in Globally Coupled Oscillators: Robustness and Occurrence through Delayed Coupling [PDF]
, 2001 The phenomenon of slow switching in populations of globally coupled oscillators is discussed. This characteristic collective dynamics, which was first discovered in a particular class of the phase oscillator model, is a result of the formation of a ...
A.T. Winfree +18 more
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Singular Orbits and Dynamics at Infinity of a Conjugate Lorenz-Like System
Mathematical Modelling and Analysis, 2015 A conjugate Lorenz-like system which includes only two quadratic nonlinearities is proposed in this paper. Some basic properties of this system, such as the distribution of its equilibria and their stabilities, the Lyapunov exponents, the bifurcations ...
Fengjie Geng, Xianyi Li
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Spiralling dynamics near heteroclinic networks [PDF]
, 2013 There are few explicit examples in the literature of vector fields exhibiting complex dynamics that may be proved analytically. We construct explicitly a {two parameter family of vector fields} on the three-dimensional sphere $\EU^3$, whose flow has a ...
Address Of Alex +7 more
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Heteroclinic Dynamics of Localized Frequency Synchrony: Stability of Heteroclinic Cycles and Networks [PDF]
Journal of Nonlinear Science, 2019 In the first part of this paper, we showed that three coupled populations of identical phase oscillators give rise to heteroclinic cycles between invariant sets where populations show distinct frequencies. Here, we now give explicit stability results for these heteroclinic cycles for populations consisting of two oscillators each.
Christian Bick, Alexander Lohse
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Shapley Polygons in 4 x 4 Games
Games, 2010 We study 4 x 4 games for which the best response dynamics contain a cycle. We give examples in which multiple Shapley polygons occur for these kinds of games.
Martin Hahn
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The Hunt Opinion Model-An Agent Based Approach to Recurring Fashion Cycles. [PDF]
PLoS ONE, 2016 We study a simple agent-based model of the recurring fashion cycles in the society that consists of two interacting communities: "snobs" and "followers" (or "opinion hunters", hence the name of the model).
Rafał Apriasz +3 more
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On Takens' Last Problem: tangencies and time averages near heteroclinic networks [PDF]
, 2017 We obtain a structurally stable family of smooth ordinary differential equations exhibiting heteroclinic tangencies for a dense subset of parameters. We use this to find vector fields $C^2$-close to an element of the family exhibiting a tangency, for ...
Labouriau, Isabel S. +1 more
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Criteria for robustness of heteroclinic cycles in neural microcircuits [PDF]
The Journal of Mathematical Neuroscience, 2011 We introduce a test for robustness of heteroclinic cycles that appear in neural microcircuits modeled as coupled dynamical cells. Robust heteroclinic cycles (RHCs) can appear as robust attractors in Lotka-Volterra-type winnerless competition (WLC) models as well as in more general coupled and/or symmetric systems.
Ashwin, Peter +2 more
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