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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...
Periodic Orbits of Vector Fields: Computational Challenges
Computational Challenges Vector Fields
2015/8/25
Simulation of vector elds is ubiquitous: examples occur in every discipline of
science and engineering. Periodic orbits are frequently encountered as trajectories.
We use solutions of initial value...
Exponential Dichotomies and Homoclinic Orbits from Heteroclinic Cycles
Exponential Dichotomies Homoclinic Orbits Heteroclinic Cycle Melnikov Function
2013/1/30
In this paper, we investigate the homoclinic bifurcations from a heteroclinic cycle by using exponential dichotomies.We give a Melnikov!atype condition assuring the existence ofhomoclinic orbits form ...