Abstract
This chapter investigates the energy flow characteristics of local bifurcations for nonlinear dynamical systems. Similar to the centre manifold theorem developed from the Jacobian matrix, we propose a centre energy flow theorem based on the eigenvalues of the energy flow matrix, for which two examples are given to demonstrate its applications. Four simplest energy flow bifurcations of equilibria: saddle-node, transcritical, pitchfork and Hopf ones are discussed.
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© 2015 Springer International Publishing Switzerland
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Xing, J.T. (2015). Energy Flow Characteristics of Local Bifurcations. In: Energy Flow Theory of Nonlinear Dynamical Systems with Applications. Emergence, Complexity and Computation, vol 17. Springer, Cham. https://doi.org/10.1007/978-3-319-17741-0_6
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DOI: https://doi.org/10.1007/978-3-319-17741-0_6
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-17740-3
Online ISBN: 978-3-319-17741-0
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