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2019•International Journal of Geometric Methods in Modern PhysicsRequires access

Mapping of non-autonomous dynamical systems to autonomous ones

Davood Momeni, Phongpichit Channuie, Mudhahir Al Ajmi

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Abstract

Using a proper choice of the dynamical variables, we show that a non-autonomous dynamical system transforming to an autonomous dynamical system with a certain coordinate transformations can be obtained by solving a general nonlinear first-order partial differential equations. We examine some special cases and provide particular physical examples. Our framework constitutes general machineries in investigating other non-autonomous dynamical systems.

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What this paper is about

Using a proper choice of the dynamical variables, we show that a non-autonomous dynamical system transforming to an autonomous dynamical system with a certain coordinate transformations can be obtained by solving a general nonlinear first-order partial differential equations. We examine some special cases and provide particular physical examples. Our framework constitutes general machineries in investigating other non-autonomous dynamical systems.

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Available abstract

Using a proper choice of the dynamical variables, we show that a non-autonomous dynamical system transforming to an autonomous dynamical system with a certain coordinate transformations can be obtained by solving a general nonlinear first-order partial differential equations. We examine some special cases and provide particular physical examples. Our framework constitutes general machineries in investigating other non-autonomous dynamical systems.

Key concepts: Dynamical systems theory, Autonomous system (mathematics), Dynamical system (definition), Nonlinear dynamical systems, Nonlinear system, Projected dynamical system, Linear dynamical system, Partial differential equation

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