Sunday, December 29, 2019

Non Linear Behaviour And Chaos - 1277 Words

ABSTRACT In this report non-linear behaviour and chaos have been explored through Duffing Equation computationally. Key features of the chaos theory such as attractors, Poincarà ¨ sections and phase-space diagrams have been analysed and discussed. The programing language of choice for this experiment was Fortran 90, which has been written explicitly for the purposes of acquiring a chaotic system and solving the Duffing equation. Introduction The Duffing Oscillator named by the German electrical engineer Georg Duffing is a non-linear, second-order differential equation, periodically forced and includes a damping term proportional to particle’s velocity. The equation can show different types of oscillations such as a limit cycles and chaos. Given its characteristics Duffing oscillators are often used to produce similar behaviours in nature. The equation in this experiment has been studied through the dynamics of a particle under a potential field, driven by an applied periodical force. The equation of motion for the particle in this system is (1) Where constant A gives the strength of a non-linear term, B gives the strength of the linear term, C controls the size of damping, D controls the periodic driving force, and ω is the driving frequency. The changes in the environment caused by the periodic force are sufficient to lead a chaotic behaviour, as is the case with Duffing Oscillators. Most of the systems in universe have a non-linear nature. Although a majority ofShow MoreRelatedKurt Lewin and complexity theories: back to the future?7984 Words   |  32 Pagesseen as outmoded and irrelevant to the needs of modem organizations. It might be expected that this tendency would increase as academics and practitioners draw on the work of complexity theorists to portray organizations as complex, dynamic, non-linear self-organizing systems. 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