Indian Journal of Science and Technology
Year: 2018, Volume: 11, Issue: 21, Pages: 1-7
Pedro Pablo Cárdenas Alzate1*, José Gerardo Cardona Toro2 and Luz María Rojas Duque3
1 Departamento de Matemáticas and Research Group GEDNOL, Universidad Tecnológica de Pereira, Pereira, Colombia; [email protected]
2 Departamento de Matemáticas, Universidad Tecnológica de Pereira, Pereira, Colombia; [email protected]
3 Fundación Universitaria del Área Andina, Pereira, Colombia; [email protected]
*Author for correspondence
Pedro Pablo Cárdenas Alzate,
Departamento de Matemáticas and Research Group GEDNOL, Universidad Tecnológica de Pereira, Pereira, Colombia; [email protected]
Objective: To determine the exponents of Lyapunov for a system with unknown dynamics. Methods: The determination of chaos presence in any system have a great importance to right analysis, thus there are indicators that permit quantifying this phenomenon, one of them and perhaps more relevant are the Lyapunov exponents. That is why this paper presents a methodology to calculate these quantifiers from the system dynamically. (differentials equations). Findings: In many occasions, we know the system dynamics, but we do not have necessary instruments to measure all the present states, thus we need to reconstructthe phase space from the times series scalar that we have. If one wants to analyze the original dynamics of the dynamic system from the said series, the attractor in the multivariable space is necessary, which is known as reconstruction of the phase space, originally proposed by Ruelle. This technique converts a scalar series x (t) in a vector v of dimension m (Embedding dimension) using a delay time. Application: As mentioned, in various physical situations there is no measurement of all the variables of the system’s state, therefore, it is necessary to reconstruct the dynamics of the system from the available measurements. Assuming that only the voltage measurement of capacitor one (Vc1) is available from the Chua circuit.
Keywords: Chua Circuit, Embedment Dimension, Exponents of Lyapunov, Multivariable Dynamic System, Phase Space
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