Control and Chaos

1. Front Matter

   Pages i-viii

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2. Understanding Complex Dynamics

   1. Triangulating Noisy Dynamical Systems

      • Stuart Allie, Alistair Mees, Kevin Judd, Dave Watson

      Pages 1-11

   2. Attractor Reconstruction and Control Using Interspike Intervals

      • Tim Sauer

      Pages 12-24

   3. Modeling Chaos from Experimental Data

      • Kevin Judd, Alistair Mees

      Pages 25-38

   4. Chaos in Symplectic Discretizations of the Pendulum and Sine-Gordon Equations

      • B. M. Herbst, C. M. Schober

      Pages 39-59

   5. Collapsing Effects in Computation of Dynamical Systems

      • Phil Diamond, Peter Kloeden, Aleksej Pokrovskii

      Pages 60-90

   6. Bifurcations in the Falkner-Skan equation

      • Colin Sparrow

      Pages 91-105

   7. Some Characterisations of Low-dimensional Dynamical Systems with Time-reversal Symmetry

      • John A. G. Roberts

      Pages 106-133

3. Controlling Complex Systems

   1. Control of Chaos by Means of Embedded Unstable Periodic Orbits

      • Edward Ott, Brian R. Hunt

      Pages 134-141

   2. Notch Filter Feedback Control for k-Period Motion in a Chaotic System

      • Walter J. Grantham, Amit M. Athalye

      Pages 142-157

   3. Targeting and Control of Chaos

      • Eric J. Kostelich, Ernest Barreto

      Pages 158-169

   4. Adaptive Nonlinear Control: A Lyapunov Approach

      • Petar V. Kokotović, Miroslav Krstić

      Pages 170-182

   5. Creating and Targeting Periodic Orbits

      • Kathryn Glass, Michael Renton, Kevin Judd, Alistair Mees

      Pages 183-196

   6. Dynamical Systems, Optimization, and Chaos

      • John B. Moore

      Pages 197-206

   7. Combined Controls for Noisy Chaotic Systems

      • Mirko Paskota, Kok Lay Teo, Alistair Mees

      Pages 207-225

   8. Complex Dynamics in Adaptive Systems

      • Iven M. Y. Mareels

      Pages 226-250

   9. Hitting Times to a Target for the Baker’s Map

      • Arthur Mazer

      Pages 251-259

4. Applications

   1. Controllable Targets Near a Chaotic Attractor

      • Thomas L. Vincent

      Pages 260-277

   2. The Dynamics of Evolutionary Stable Strategies

      • Yosef Cohen, Thomas L. Vincent

      Pages 278-303

   3. Nitrogen Cycling and the Control of Chaos in a Boreal Forest Model

      • John Pastor, Yosef Cohen

      Pages 304-319

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.

• Nonlinear system
• bifurcation
• complex system
• complex systems
• equation
• optimization
• system

• Center for Applied Dynamics and Optimization, Department of Mathematics, The University of Western Australia, Perth, Australia

  Kevin Judd, Alistair Mees, Kok Lay Teo

• Aerospace and Mechanical Engineering, University of Arizona, Tucson, USA

  Thomas L. Vincent

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