Control and Chaos
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Control and Chaos

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Kevin Judd
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Understanding Complex Dynamics.- Triangulating Noisy Dynamical Systems.- Attractor Reconstruction and Control Using Interspike Intervals.- Modeling Chaos from Experimental Data.- Chaos in Symplectic Discretizations of the Pendulum and Sine-Gordon Equations.- Collapsing Effects in Computation of Dynamical Systems.- Bifurcations in the Falkner-Skan equation.- Some Characterisations of Low-dimensional Dynamical Systems with Time-reversal Symmetry.- Controlling Complex Systems.- Control of Chaos by Means of Embedded Unstable Periodic Orbits.- Notch Filter Feedback Control for k-Period Motion in a Chaotic System.- Targeting and Control of Chaos.- Adaptive Nonlinear Control: A Lyapunov Approach.- Creating and Targeting Periodic Orbits.- Dynamical Systems, Optimization, and Chaos.- Combined Controls for Noisy Chaotic Systems.- Complex Dynamics in Adaptive Systems.- Hitting Times to a Target for the Baker's Map.- Applications.- Controllable Targets Near a Chaotic Attractor.- The Dynamics of Evolutionary Stable Strategies.- Nitrogen Cycling and the Control of Chaos in a Boreal Forest Model.- Self-organization Dynamics in Chaotic Neural Networks.
This volume contains the proceedings of the US-Australia workshop on Control and Chaos held in Honolulu, Hawaii from 29 June to 1 July, 1995. The workshop was jointly sponsored by the National Science Foundation (USA) and the Department of Industry, Science and Technology (Australia) under the US-Australia agreement. Control and Chaos-it brings back memories of the endless reruns of "Get Smart" where the good guys worked for Control and the bad guys were associated with Chaos. In keeping with current events, Control and Chaos are no longer adversaries but are now working together. In fact, bringing together workers in the two areas was the focus of the workshop. The objective of the workshop was to bring together experts in dynamical systems theory and control theory, and applications workers in both fields, to focus on the problem of controlling nonlinear and potentially chaotic systems using limited control effort. This involves finding and using orbits in nonlinear systems which can take a system from one region of state space to other regions where we wish to stabilize the system. Control is used to generate useful chaotic trajectories where they do not exist, and to identify and take advantage of useful ones where they do exist. A controller must be able to nudge a system into a proper chaotic orbit and know when to come off that orbit. Also, it must be able to identify regions of state space where feedback control will be effective.