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Dynamics of the solution of Bratu’s equation. (English) Zbl 1238.34073
Summary: We examine the dynamics exhibited by the solution of Bratu’s equation. It represents a one-dimensional map with control parameter $\theta $. For certain values of the parameter $\theta $ it exhibits successive bifurcations and shows chaotic regimes. This behaviour was confirmed by calculating the corresponding Lyapunov exponent, power spectra and cobweb diagrams, indicating similarities with other well-known one-dimensional maps.

MSC:
34C23Bifurcation (ODE)
34C28Complex behavior, chaotic systems (ODE)
37D45Strange attractors, chaotic dynamics
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References:
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