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Dressed return maps distinguish chaotic mechanisms
Physical Review E, 2013Chaotic data generated by a three-dimensional dynamical system can be embedded into R(3) in a number of inequivalent ways. However, when lifted into R(5) they all become equivalent, indicating that they all belong to a single universality class sharing a common chaos-generating mechanism.
Daniel J, Cross, R, Gilmore
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Return mapping for nonsmooth and multiscale elastoplasticity
Computer Methods in Applied Mechanics and Engineering, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tu, Xuxin +2 more
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An Improved Return Maps Method for Parameter Estimation of Chaotic Systems
International Journal of Bifurcation and Chaos, 2020Recently, an effective method called return maps is proposed for the parameter estimation of chaotic systems. However, high time-consumption limits practical applications. In this paper, we focus on this problem, and an improved return maps method is proposed. It combines the differential evolution algorithm with the return maps method, and simplifies
Yuexi Peng, Kehui Sun, Shaobo He 0001
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Approximate return maps for quadrupedal running
Proceedings of International Conference on Robotics and Automation, 2002This paper describes approximate return maps for the bound and pronk gaits in a simple quadruped model. Although expressions for the exact maps cannot be obtained, perturbation theory allows derivation of explicit expressions for approximate maps if particular parameters are assumed small.
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First return map and invariant measures
Israel Journal of Mathematics, 1980We give sufficient conditions for the existence of absolutely continuous invariant measures, finite or σ-finite, for maps on the interval. We givea priori bound for the number of different ergodic measures. The results are obtained via the first return map.
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Analysis of hybrid systems by means of embedded return maps
2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512), 2004The behavioural analysis of hybrid systems is to a large extend an open problem. In this paper it is shown how the construction of an embedded map can be used to determine the characteristics of the output signal of a hybrid system. The method is demonstrated with two DC-DC converter examples.
Jörg Krupar +2 more
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Return maps in cyclotomic piecewise similarities
Dynamical Systems, 2005Let p > 2 be prime or twice an odd prime. We prove that the first return cyclotomic-integer piecewise similarity or order p is also an integer piecewise similarity. Moreover, we show that all cells of an integer piecewise similarity are spanned by integers in .
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2017
The Poincare return map is a model for measuring changes in trajectories and for evaluating the effects of forces that facilitate or present barriers to the pathways. It is important to measure the stability of a trajectory or its deviation. With either situation, one seeks to understand the variables that maintain stability or that generate the ...
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The Poincare return map is a model for measuring changes in trajectories and for evaluating the effects of forces that facilitate or present barriers to the pathways. It is important to measure the stability of a trajectory or its deviation. With either situation, one seeks to understand the variables that maintain stability or that generate the ...
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The displacement function and the return map
2011This chapter studies the displacement function dᵧ on X that is associated with a semisimple element γ ∈ G. If φ″, t ∈ R denotes the geodesic flow on the total space X of the tangent bundle of X, the critical set X(γ) ⊂ X of dᵧ can be easily related to the fixed point set Fᵧ ⊂ X of the symplectic transformation γ⁻¹φ₁ of X.
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Return maps of folded nodes and folded saddle-nodes
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2008Folded nodes occur in generic slow-fast dynamical systems with two slow variables. Open regions of initial conditions flow into a folded node in an open set of such systems, so folded nodes are an important feature of generic slow-fast systems. Twisting and linking of trajectories in the vicinity of a folded node have been studied previously, but their
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