Advanced Materials Science Research

Chaotic Modeling And Simulation

 Chaotic modeling and simulation is a fast growing field that influences the world around us, and consequently also influences our ways of approaching, analyzing and solving problems. In this paper the rotation–translation case is presented based on the theory analyzed in the book — Chaotic Modeling and Simulation: Analysis of Chaotic Models, Attractors and Forms published by the above authors [Skiadas & Skiadas, 2008]. An overview of the chaotic flows in rotation–translation is given. Special cases and illustrations of chaotic attractors and forms are presented and a method of comparative presentation and analysis of the flows by using both continuous and discrete methods is applied by deriving the appropriate differential and difference equations' analogue. Furthermore, an analysis of chaotic attractors resulting in the models proposed is given along with an exploration of the characteristic or equilibrium points. Modeling and simulation of nonlinear systems under chaotic behavior is presented. Nonlinear systems and their relation to chaos as a result of nonlinear interaction of different elements in the system are presented. Application of chaotic theory for power systems is discussed through simulation results. Simulation of some mathematical equations, e.g. Vander Pol's equation, Lorenz's equation, Duffing's equation and double scroll equations are presented. Theoretical aspects of dynamical systems, the existence of chaos in power system and their dependency on system parameters and initial conditions using computer simulations are discussed. From the results one can easily understand the strange attractor and transient stages to voltage collapse, angle instability or voltage collapse and angle divergence simultaneously. Important simulation results of chaos for a model three bus system are presented and discussed.  

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