WebDynamical billiards are paradigmatic examples of chaotic Hamiltonian dynamical systems with widespread applications in physics. We study how well their Lyapunov exponent, characterizing the chaotic dynamics, and its dependence on external parameters can be estimated from phase space volume arguments, with emphasis on billiards with mixed … WebPhase synchronization occurs when the coupled chaotic oscillators keep their phase difference bounded while their amplitudes remain uncorrelated. This phenomenon occurs even if the oscillators are not identical. Observation of phase synchronization requires a previous definition of the phase of a chaotic oscillator.

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Web1 day ago · In Fig. 2, Fig. 3, we draw 2D phase portrait, 3D phase portrait, Poincaré section and sensitivity analysis of (18) for different parameters. From Fig. 2 c, we can conclude that system (18) is chaotic owing to the fact that the Poincaré section of (18) is a dense point in pieces and has a WebPhase space is a way to visualize dynamic systems that have complex movements to them. We like to have the x-axis be position and the y-axis be either momentum or velocity, for … boys looking after cattles

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WebJul 1, 2009 · Chaotic phase synchronization takes place in cases involving almost identical dynamical systems and it means that the phase difference between the systems is kept bounded over the time, while their amplitudes remain chaotic and may be uncorrelated. Web1 day ago · In Fig. 2, Fig. 3, we draw 2D phase portrait, 3D phase portrait, Poincaré section and sensitivity analysis of (18) for different parameters. From Fig. 2 c, we can conclude … WebChaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization. [2] boys love anicloud