Ebook: Control and Chaos

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.

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Content:
Front Matter....Pages i-viii
Triangulating Noisy Dynamical Systems....Pages 1-11
Attractor Reconstruction and Control Using Interspike Intervals....Pages 12-24
Modeling Chaos from Experimental Data....Pages 25-38
Chaos in Symplectic Discretizations of the Pendulum and Sine-Gordon Equations....Pages 39-59
Collapsing Effects in Computation of Dynamical Systems....Pages 60-90
Bifurcations in the Falkner-Skan equation....Pages 91-105
Some Characterisations of Low-dimensional Dynamical Systems with Time-reversal Symmetry....Pages 106-133
Control of Chaos by Means of Embedded Unstable Periodic Orbits....Pages 134-141
Notch Filter Feedback Control for k-Period Motion in a Chaotic System....Pages 142-157
Targeting and Control of Chaos....Pages 158-169
Adaptive Nonlinear Control: A Lyapunov Approach....Pages 170-182
Creating and Targeting Periodic Orbits....Pages 183-196
Dynamical Systems, Optimization, and Chaos....Pages 197-206
Combined Controls for Noisy Chaotic Systems....Pages 207-225
Complex Dynamics in Adaptive Systems....Pages 226-250
Hitting Times to a Target for the Baker’s Map....Pages 251-259
Controllable Targets Near a Chaotic Attractor....Pages 260-277
The Dynamics of Evolutionary Stable Strategies....Pages 278-303
Nitrogen Cycling and the Control of Chaos in a Boreal Forest Model....Pages 304-319
Self-organization Dynamics in Chaotic Neural Networks....Pages 320-333

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Content:
Front Matter....Pages i-viii
Triangulating Noisy Dynamical Systems....Pages 1-11
Attractor Reconstruction and Control Using Interspike Intervals....Pages 12-24
Modeling Chaos from Experimental Data....Pages 25-38
Chaos in Symplectic Discretizations of the Pendulum and Sine-Gordon Equations....Pages 39-59
Collapsing Effects in Computation of Dynamical Systems....Pages 60-90
Bifurcations in the Falkner-Skan equation....Pages 91-105
Some Characterisations of Low-dimensional Dynamical Systems with Time-reversal Symmetry....Pages 106-133
Control of Chaos by Means of Embedded Unstable Periodic Orbits....Pages 134-141
Notch Filter Feedback Control for k-Period Motion in a Chaotic System....Pages 142-157
Targeting and Control of Chaos....Pages 158-169
Adaptive Nonlinear Control: A Lyapunov Approach....Pages 170-182
Creating and Targeting Periodic Orbits....Pages 183-196
Dynamical Systems, Optimization, and Chaos....Pages 197-206
Combined Controls for Noisy Chaotic Systems....Pages 207-225
Complex Dynamics in Adaptive Systems....Pages 226-250
Hitting Times to a Target for the Baker’s Map....Pages 251-259
Controllable Targets Near a Chaotic Attractor....Pages 260-277
The Dynamics of Evolutionary Stable Strategies....Pages 278-303
Nitrogen Cycling and the Control of Chaos in a Boreal Forest Model....Pages 304-319
Self-organization Dynamics in Chaotic Neural Networks....Pages 320-333
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