Driving trajectories in complex systems

A new paradigm, which combines targeting type of control problem for chaotic systems with the techniques used in system control theory, is proposed. This paradigm is used to rapidly change the evolution of a complex system among desired behaviors. We point out how this paradigm can also be applied to nonlinear systems that do not present the characteristics of a complex system.

[1]  P. Rapp,et al.  The algorithmic complexity of neural spike trains increases during focal seizures , 1994, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[2]  Grebogi,et al.  Self-organization and chaos in a fluidized bed. , 1995, Physical review letters.

[3]  Giacomelli,et al.  Experimental evidence of chaotic itinerancy and spatiotemporal chaos in optics. , 1990, Physical review letters.

[4]  G. Zaslavsky.  The simplest case of a strange attractor , 1978 .

[5]  Grebogi,et al.  Using chaos to direct trajectories to targets. , 1990, Physical review letters.

[6]  Young,et al.  Inferring statistical complexity. , 1989, Physical review letters.

[7]  Celso Grebogi,et al.  Basin boundary metamorphoses: changes in accessible boundary orbits , 1987 .

[8]  John Horgan,et al.  From Complexity to Perplexity , 1995 .

[9]  Schmidt,et al.  Dissipative standard map. , 1985, Physical review. A, General physics.

[10]  C. Grebogi,et al.  Multistability and the control of complexity. , 1997, Chaos.

[11]  B. Chirikov.  A universal instability of many-dimensional oscillator systems , 1979 .

[12]  H. Abarbanel,et al.  Correlations of periodic, area-preserving maps , 1983 .

[13]  G. Schmidt.  Stochasticity and fixed-point transitions , 1980 .

[14]  John M. Greene,et al.  A method for determining a stochastic transition , 1979, Hamiltonian Dynamical Systems.

[15]  Celso Grebogi,et al.  Multiple coexisting attractors, basin boundaries and basic sets , 1988 .

[16]  Y. Lai,et al.  Controlling chaotic dynamical systems , 1997 .

[17]  M. Dubois,et al.  Transient reemergent order in convective spatial chaos , 1983 .

[18]  Grebogi,et al.  Map with more than 100 coexisting low-period periodic attractors. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.