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Conservative homoclinic bifurcations and some applications
conservative dynamics homoclinic bifurcations Newhouse phenomena persistent tangencies Hausdorff dimension standard map three body problem Sitnikov problem
2015/9/25
We study generic unfoldings of homoclinic tangencies of two dimensional area preserving diffeomorphisms (conservative Newhouse phenomena) and show that they give rise to invariant hyperbolic sets of a...
Hopf Bifurcations in Two-Player Delayed Replicator Dynamics
Hopf Bifurcations Two-Player Delayed Replicator Dynamics
2015/8/26
We investigate the dynamics of two-strategy replicator equa-tions in which competition between strategies is delayed by a given time interval T. Taking T as a bifurcation parameter, we demonstrate the...
Hopf Bifurcations in Delayed Rock–Paper–Scissors Replicator Dynamics
Replicator Delay Hopf bifurcation Limit cycle Lindstedt
2015/8/26
We investigate the dynamics of three-strategy (rock–paper–scissors) replicator equations in which the fitness of each strategy is a function of the population frequencies delayed by a time interval T....
We are still far from a comprehensive theory of bifurcation in dynamical systems with
multiple time scales. However, systematic application of geometric methods and study
of examples have produced d...
Bifurcations of Relaxation Oscillations near Folded Saddles
Folded Saddles Relaxation Oscillations
2015/8/25
Relaxation oscillations are periodic orbits of multiple time scale dynamical systems
that contain both slow and fast segments. The slow-fast decomposition of these orbits is
de ned in the singular l...
Homoclinic Orbits of the FitzHugh–Nagumo Equation: Bifurcations in the Full System
homoclinic bifurcation singular perturbation
2015/8/25
This paper investigates travelling wave solutions of the FitzHugh–Nagumo equation from the viewpoint
of fast-slow dynamical systems. These solutions are homoclinic orbits of a three dimensional
vect...
Computing Periodic Orbits and their Bifurcations with Automatic Differentiation
Automatic Differentiation Computing Periodic Orbits
2015/8/25
This paper examines algorithms for computing periodic orbits of dynamical systems. Our
goal is to explore the limits of accuracy that are attainable for these calculations within
the pragmatic conte...
The Forced van der Pol Equation I: The Slow Flow and Its Bifurcations
van der Pol oscillator hybrid dynamical system
2015/8/25
The forced van der Pol oscillator has been the focus of scientific scrutiny for almost a century, yet
its global bifurcation structure is still poorly understood. In this paper, we present a hybrid s...
Bifurcations of stochastic differential equations with singular diffusion coefficients
bifurcations noise universal unfolding stochastic stability (quasi)-stationary distributions normal forms
2012/5/9
In this article, we address the dynamics and bifurcations of a wide class of stochastic differential equations around singular points where both the drift and diffusion functions vanish. We apply thes...
Periodic windows distribution resulting from homoclinic bifurcations in the two-parameter space
Homoclinic systems Periodic windows Bifurcation
2010/12/28
Periodic solution parameters, in chaotic dynamical systems, form periodic windows with characteristic distribution in two-parameter spaces. Recently, general properties of this organization have been ...
Shell structure and orbit bifurcations in finite fermion systems
Shell structure orbit bifurcations finite fermion systems
2011/3/2
We first give an overview of the shell-correction method which was developed by V. M.Strutinsky as a practicable and efficient approximation to the general selfconsistent theory of finite fermion syst...
Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon/mechanism for diffeomorphisms
Essential hyperbolicity homoclinic bifurcations dichotomy phenomenon/mechanism for diffeomorphisms
2010/11/22
We prove that any diffeomorphism of a compact manifold can be approximated in topology C1 by another diffeomorphism exhibiting a homoclinic bifurcation (a homoclinic tangency or a heterodimensional c...
Analytic and algebraic conditions for bifurcations of homoclinic orbits I: Saddle equilibria
Homoclinic orbit bifurcation Differential Galois theory Melnikov method
2010/11/30
We study bifurcations of homoclinic orbits to hyperbolic saddle equilibria in a class of four-dimensional systems which may be Hamil-tonian or not. Only one parameter is enough to treat these types of...
On riddled sets and bifurcations of chaotic attractors
Riddling basins coupled maps blow out bifurcations
2010/9/15
Coupled systems provide us examples of blowout bifurcations and these maps have parameter values at which there are attractors which are a filled-in quadrilateral and, simultaneously, the synchronized...
A single-axis flux decay model including an excitationcontrol model proposed in [12,14,16] is studied. As thebifurcation parameter $P_{m}$ (input power to the generator)varies, the system exhibits dyn...