Results 71 to 80 of about 6,100 (243)
Heteroclinic cycles emanating from local bifurcations
Manuscripta Mathematica, 1994 The paper deals with a two-parameter system of ordinary differential equations on \(\mathbb{R}^ n\) \((1) : \dot x = f(x, \lambda, \alpha)\), where \(f\) is \(Z_ 2\)-symmetric, i.e. there exists a linear mapping \(g : \mathbb{R}^ n \to \mathbb{R}^ n\) such that \(g^ 2 = I\), \(g \neq I\) and \(gf(x, \lambda, \alpha) = f(gx, \lambda, \alpha)\) for all \(
Wu, Wei, Zou, Yongkui, Huang, Mingyou
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Mathematical Methods in the Applied Sciences, Volume 48, Issue 12, Page 12011-12037, August 2025.ABSTRACT In bio‐social models, cooperative behavior has evolved as an adaptive strategy, playing multi‐functional roles. One of such roles in populations is to increase the success of the survival and reproduction of individuals and their families or social groups.
Sangeeta Saha +2 more
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Dense heteroclinic tangencies near a Bykov cycle [PDF]
, 2014 This article presents a mechanism for the coexistence of hyperbolic and non-hyperbolic dynamics arising in a neighbourhood of a Bykov cycle where trajectories turn in opposite directions near the two nodes --- we say that the nodes have different ...
Labouriau, Isabel S. +1 more
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Studies in Applied Mathematics, Volume 155, Issue 2, August 2025.ABSTRACT We develop a general modeling framework for compartmental epidemiological systems structured by continuous variables which are linked to the levels of expression of compartment‐specific traits. We start by formulating an individual‐based model that describes the dynamics of single individuals in terms of stochastic processes. Then, we formally
Emanuele Bernardi +3 more
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Journal of Engineering, 2015 Based on the heteroclinic Shil’nikov theorem and switching control, a kind of multipiecewise linear chaotic system is constructed in this paper. Firstly, two fundamental linear systems are constructed via linearization of a chaotic system at its two ...
Chunyan Han, Fang Yuan, Xiaoyuan Wang
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Stability of N‐front and N‐back solutions in the Barkley model
GAMM-Mitteilungen, Volume 48, Issue 1, March 2025.ABSTRACT In this article, we establish for an intermediate Reynolds number domain the stability of N$$ N $$‐front and N$$ N $$‐back solutions for each N>1$$ N>1 $$ corresponding to traveling waves, in an experimentally validated model for the transition to turbulence in pipe flow proposed in [Barkley et al., Nature 526(7574):550‐553, 2015]. We base our
Christian Kuehn, Pascal Sedlmeier
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Bifurcation analysis of a three dimensional system
Journal of Hebei University of Science and Technology, 2018 In order to enrich the stability and bifurcation theory of the three dimensional chaotic systems, taking a quadratic truncate unfolding system with the triple singularity equilibrium as the research subject, the existence of the equilibrium, the ...
Yongwen WANG, Zhiqin QIAO, Yakui XUE
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Effect of Noise on Excursions To and Back From Infinity
, 2001 The effect of additive white noise on a model for bursting behavior in large aspect-ratio binary fluid convection is considered. Such bursts are present in systems with nearly square symmetry and are the result of heteroclinic cycles involving infinite ...
Ashwin +31 more
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Bifurcations and dynamics in convection with temperature-dependent viscosity in the presence of the O(2) symmetry [PDF]
, 2013 We focus the study of a convection problem in a 2D setup in the presence of the O(2) symmetry. The viscosity in the fluid depends on the temperature as it changes its value abruptly in an interval around a temperature of transition.
Curbelo, Jezabel, Mancho, Ana M.
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A Multiparameter Singular Perturbation Analysis of the Robertson Model
Studies in Applied Mathematics, Volume 154, Issue 2, February 2025.ABSTRACT The Robertson model describing a chemical reaction involving three reactants is one of the classical examples of stiffness in ODEs. The stiffness is caused by the occurrence of three reaction rates k1,k2,${k}_{1},{k}_{2},$ and k3,${k}_{3},$ with largely differing orders of magnitude, acting as parameters.
Lukas Baumgartner, Peter Szmolyan
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