Chaos and Synchronization

Jan Awrejcewicz
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Jan Awrejcewicz: Łódź University of Technology, Department of Automation, Biomechanics and Mechatronics

Chapter Chapter 15 in Ordinary Differential Equations and Mechanical Systems, 2014, pp 527-604 from Springer

Abstract: Abstract New point of view, introduced into known definitions in mathematic and empiric sciences by developments in nonlinear dynamic, provides novel interpretations of one of many philosophical trends based on determinism and indeterminism. Until now those two concepts were treated as mutually exclusive; however examples of chaotic motions appearing in a simple physical, chemical or biological systems indicate possibility that relationship between them exists. Even though, theoretically, the determination of motion trajectory is possible by the introduction of the highly accurate initial conditions, obtaining sufficient accuracy is impossible in practice. This issue has much wider range, and as every real state of system is described with a certain inaccuracy, it should be described as probability distribution and not as numbers. This is the reason why in determined system we expect typical for stochastic systems dynamics (it will be described and illustrated for a simple mapping and ordinary differential equations further). This type of deterministic systems motion, contrary to random variable systems, is called deterministic chaos.

Keywords: Periodic Orbit; Lyapunov Exponent; Phase Portrait; Chaotic Dynamic; Chaotic Attractor (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-07659-1_15

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DOI: 10.1007/978-3-319-07659-1_15

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