Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

From Wikipedia, the free encyclopedia. John Mark Guckenheimer. Baton Rouge , Louisiana.

Cornell University. Archived from the original on Retrieved Namespaces Article Talk. Views Read Edit View history. In other projects Wikimedia Commons. By using this site, you agree to the Terms of Use and Privacy Policy. Dynamical systems Bifurcation theory. Guckenheimer, J.

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

Springer-Verlag, New York. ABSTRACT: This paper discusses a novel technique and implementation to perform nonlinear control for two different forced model state oscillators and actuators. The paper starts by discussing the Duffing oscillator which features a second order non-linear differential equation describing complex motion whereas the second model is the Van der Pol oscillator with non-linear damping.


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A first order actuator is added to both models to expand on the chaotic behavior of the oscillators. In order to control the system without comprising linearization, Lyapunov non-linear control was used. A control Lyapunov function was tailored to the system.

This led to improved maneuverability of the controller and the performance of the overall system. The controller was found to be highly efficient in system tracking and had swift response time. Simulations were performed on both the uncontrolled and controlled cases. Both simulation results ultimately confirmed the effectiveness of the proposed controller.


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