Results 31 to 40 of about 645,356 (284)
Bifurcations of a Homoclinic Orbit to Saddle-Center in Reversible Systems
Abstract and Applied Analysis, 2012 The bifurcations near a primary homoclinic orbit to a saddle-center are investigated in a 4-dimensional reversible system. By establishing a new kind of local moving frame along the primary homoclinic orbit and using the Melnikov functions, the existence
Zhiqin Qiao, Yancong Xu
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On the distribution of periodic orbits
Discrete and Continuous Dynamical Systems, 2010 Let $f:M\to M$ be a $C^{1+ε}$-map on a smooth Riemannian manifold $M$ and let $Λ\subset M$ be a compact $f$-invariant locally maximal set. In this paper we obtain several results concerning the distribution of the periodic orbits of $f|Λ$. These results are non-invertible and, in particular, non-uniformly hyperbolic versions of well-known results by ...
Gelfert, Katrin, Wolf, Christian
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Global orbit of a complicated nonlinear system with the global dynamic frequency method
Journal of Low Frequency Noise, Vibration and Active Control, 2021 Global orbits connect the saddle points in an infinite period through the homoclinic and heteroclinic types of manifolds. Different from the periodic movement analysis, it requires special strategies to obtain expression of the orbit and detect the ...
Zhixia Wang +3 more
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Abstract and Applied Analysis, 2013 This paper is mainly concerned with the existence, stability, and bifurcations of periodic solutions of a certain scalar impulsive differential equations on Moebius stripe.
Yefeng He, Yepeng Xing
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Resonant Homoclinic Flips Bifurcation in Principal Eigendirections
Abstract and Applied Analysis, 2013 A codimension-4 homoclinic bifurcation with one orbit flip and one inclination flip at principal eigenvalue direction resonance is considered. By introducing a local active coordinate system in some small neighborhood of homoclinic orbit, we get the ...
Tiansi Zhang, Xiaoxin Huang, Deming Zhu
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Measuring scars of periodic orbits
Physical Review E, 1999 The phenomenon of periodic orbit scarring of eigenstates of classically chaotic systems is attracting increasing attention. Scarring is one of the most important "corrections" to the ideal random eigenstates suggested by random matrix theory. This paper discusses measures of scars and in so doing also tries to clarify the concepts and effects of ...
Kaplan, L., Heller, E. J.
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Piecewise expanding maps: combinatorics, dynamics and representation of rational numbers
ESAIM: Proceedings and Surveys, 2014 We establish combinatorial properties of the dynamics of piecewise increasing, continuous, expanding maps of the interval such as description of periodic and pre-periodic points, primitiveness of truncated itineraries and length of ...
Serpa Cristina, Buescu Jorge
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Periodic and homoclinic orbits in a toy climate model [PDF]
Nonlinear Processes in Geophysics, 1994 A two dimensional system of autonomous nonlinear ordinary differential equations models glacier growth and temperature changes on an idealized planet.
M. Toner, A. D. Kirwan, Jr.
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Bifurcations of Nontwisted Heteroclinic Loop with Resonant Eigenvalues
The Scientific World Journal, 2014 By using the foundational solutions of the linear variational equation of the unperturbed system along the heteroclinic orbits to establish the local coordinate systems in the small tubular neighborhoods of the heteroclinic orbits, we study the ...
Yinlai Jin +5 more
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A Lycaon pictus impulsive state feedback control model with Allee effect and continuous time delay
Advances in Difference Equations, 2018 Allee effect (i.e. sparse effect) is active when the population density is small. Our purpose is to study such an effect of this phenomenon on population dynamics.
Yaning Li, Huidong Cheng, Yanhui Wang
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