In this thesis is to describe the use of the Poincaré-Melnikov method in the detection of homoclinic phenomena, and hence chaotic dynamics. After a short review of the theory of dynamical system, it is introduced the Poincaré-Melnikov method and its extension to the case of heteroclinic orbits. An application of this method is given in the last chapter, where it is shown a case of success and a case of failure in the detection of chaos. Results are confirmed through numerical evidence.
Homoclinic chaos and the Poincaré-Melnikov method
Azzari, Paride
2016/2017
Abstract
In this thesis is to describe the use of the Poincaré-Melnikov method in the detection of homoclinic phenomena, and hence chaotic dynamics. After a short review of the theory of dynamical system, it is introduced the Poincaré-Melnikov method and its extension to the case of heteroclinic orbits. An application of this method is given in the last chapter, where it is shown a case of success and a case of failure in the detection of chaos. Results are confirmed through numerical evidence.File in questo prodotto:
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https://hdl.handle.net/20.500.12608/28093