Results 101 to 110 of about 8,177 (202)
Practical initialization of homoclinic orbits from a Bogdanov-Takens point [PDF]
, 2014 In a recent paper [IJBC, 24(04):1450057, 2014], we improved the theoretical base for the initialization of homoclinic orbits. However, practical application of this method is not very robust without the consideration of some numerical issues.
Al-Hdaibat, Bashir +3 more
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On a Five-Dimensional Chaotic System Arising from Double-Diffusive Convection in a Fluid Layer
Abstract and Applied Analysis, 2013 A chaotic system arising from double-diffusive convection in a fluid layer is investigated in this paper based on the theory of dynamical systems. A five-dimensional model of chaotic system is obtained using the Galerkin truncated approximation.
R. Idris, Z. Siri, I. Hashim
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Bifurcation diagram for saddle/source bimodal linear dynamical systems [PDF]
, 2016 We continue the study of the structural stability and the bifurcations of planar bimodal linear dynamical systems (BLDS) (that is, systems consisting of two linear dynamics acting on each side of a straight line, assuming continuity along the separating ...
Ferrer Llop, Josep +2 more
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, 2016 Previously obtained results from the study of homoclinic bifurcations in ordinary differential equations are presented. The standard technique of analysis involves the construction of a Poincaré map on a surface near to the homoclinic point. This map is the composition of an inside map, with behaviour linearized about the homoclinic point, together ...
Drysdale, D, Drysdale, David
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Degenerate Periodic Orbits and Homoclinic Torus Bifurcation
Physical Review Letters, 2005 A one-parameter family of periodic orbits with frequency omega and energy E of an autonomous Hamiltonian system is degenerate when E'(omega) = 0. In this paper, new features of the nonlinear bifurcation near this degeneracy are identified. A new normal form is found where the coefficient of the nonlinear term is determined by the curvature of the ...
Bridges, T J, Donaldson, N M
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Homoclinic Points Calculation Method With Particle Swarm Optimization
IEEE AccessThis paper proposes a novel algorithm to accurately calculate the coordinates of homoclinic points observed in discrete-time dynamical systems. The proposed method is based on the particle swarm optimization method. Compared with the current methods, the
Tatsumi Makino +3 more
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Parametrically Excited Nonlinear Two-Degree-of-Freedom Systems with Repeated Natural Frequencies
Shock and Vibration, 1995 The method of normal forms is used to study the nonlinear response of two-degree-of-freedom systems with repeated natural frequencies and cubic nonlinearity to a principal parametric excitation.
A. H. Nayfeh, C. Chin, D. T. Mook
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, 2010 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 cycle) or by one which is essentially hyperbolic (it has
Crovisier, Sylvain, Pujals, Enrique R.
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Analysis of a Heterogeneous Trader Model for Asset Price Dynamics
Discrete Dynamics in Nature and Society, 2011 We examine an asset pricing model of Westerhoff (2005). The model incorporates heterogeneous beliefs among traders, specifically fundamentalists and trend-chasing chartists. The form of the model is shown here to be a nonlinear planar map.
Andrew Foster, Natasha Kirby
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Bifurcations of an SIRS model with generalized non-monotone incidence rate
Advances in Difference Equations, 2018 We consider an SIRS epidemic model with a more generalized non-monotone incidence: χ(I)=κIp1+Iq $\chi(I)=\frac{\kappa I^{p}}{1+I^{q}}$ with 01$, by qualitative and bifurcation analyses, we show that the model undergoes a saddle-node bifurcation, a Hopf ...
Jinhui Li, Zhidong Teng
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