EXTREME SENSITIVE DEPENDENCE ON PARAMETERS AND INITIAL CONDITIONS IN SPATIOTEMPORAL CHAOTIC DYNAMICAL-SYSTEMS

Y C LAI, R L WINSLOW, Ying-Cheng Lai

Research output: Contribution to journalArticle

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Abstract

We investigate the sensitive dependence of asymptotic attractors on both initial conditions and parameters in spatio-temporal chaotic dynamical systems. Our models of spatio-temporal systems are globally coupled two-dimensional maps and locally coupled ordinary differential equations. It is found that extreme sensitive dependence occurs commonly in both phase space and parameter space of these systems. That is, for an initial condition and/or a parameter value that leads to chaotic attractors, there are initial conditions and/or parameter values arbitrarily nearby that lead to nonchaotic attractors. This indicates the occurrence of an extreme type of fractal structure in both phase space and parameter space. A scaling exponent used to characterize extreme sensitive dependence on initial conditions and parameters is determined to be near zero in both phase space and parameter space. Accordingly, there is a significant probability of error in numerical computations intended to determine asymptotic attractors, regardless of the precision with which initial conditions or parameters are specified. Consequently, fundamental statistical properties of asymptotic attractors cannot be computed reliably for particular parameter values and initial conditions.

Original languageEnglish
Pages (from-to)353-371
Number of pages19
JournalPhysica. D, Nonlinear Phenomena
Volume74
Issue number3-4
Publication statusPublished - 15 Jul 1994

Keywords

  • FRACTAL BASIN BOUNDARIES
  • COUPLED MAP LATTICES
  • FAT FRACTALS
  • SPATIOTEMPORAL CHAOS
  • STRANGE ATTRACTOR
  • INTERMITTENCY
  • TRANSITION
  • DIMENSION
  • BEHAVIOR
  • SURFACE

Cite this

EXTREME SENSITIVE DEPENDENCE ON PARAMETERS AND INITIAL CONDITIONS IN SPATIOTEMPORAL CHAOTIC DYNAMICAL-SYSTEMS. / LAI, Y C ; WINSLOW, R L ; Lai, Ying-Cheng.

In: Physica. D, Nonlinear Phenomena, Vol. 74, No. 3-4, 15.07.1994, p. 353-371.

Research output: Contribution to journalArticle

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abstract = "We investigate the sensitive dependence of asymptotic attractors on both initial conditions and parameters in spatio-temporal chaotic dynamical systems. Our models of spatio-temporal systems are globally coupled two-dimensional maps and locally coupled ordinary differential equations. It is found that extreme sensitive dependence occurs commonly in both phase space and parameter space of these systems. That is, for an initial condition and/or a parameter value that leads to chaotic attractors, there are initial conditions and/or parameter values arbitrarily nearby that lead to nonchaotic attractors. This indicates the occurrence of an extreme type of fractal structure in both phase space and parameter space. A scaling exponent used to characterize extreme sensitive dependence on initial conditions and parameters is determined to be near zero in both phase space and parameter space. Accordingly, there is a significant probability of error in numerical computations intended to determine asymptotic attractors, regardless of the precision with which initial conditions or parameters are specified. Consequently, fundamental statistical properties of asymptotic attractors cannot be computed reliably for particular parameter values and initial conditions.",
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N2 - We investigate the sensitive dependence of asymptotic attractors on both initial conditions and parameters in spatio-temporal chaotic dynamical systems. Our models of spatio-temporal systems are globally coupled two-dimensional maps and locally coupled ordinary differential equations. It is found that extreme sensitive dependence occurs commonly in both phase space and parameter space of these systems. That is, for an initial condition and/or a parameter value that leads to chaotic attractors, there are initial conditions and/or parameter values arbitrarily nearby that lead to nonchaotic attractors. This indicates the occurrence of an extreme type of fractal structure in both phase space and parameter space. A scaling exponent used to characterize extreme sensitive dependence on initial conditions and parameters is determined to be near zero in both phase space and parameter space. Accordingly, there is a significant probability of error in numerical computations intended to determine asymptotic attractors, regardless of the precision with which initial conditions or parameters are specified. Consequently, fundamental statistical properties of asymptotic attractors cannot be computed reliably for particular parameter values and initial conditions.

AB - We investigate the sensitive dependence of asymptotic attractors on both initial conditions and parameters in spatio-temporal chaotic dynamical systems. Our models of spatio-temporal systems are globally coupled two-dimensional maps and locally coupled ordinary differential equations. It is found that extreme sensitive dependence occurs commonly in both phase space and parameter space of these systems. That is, for an initial condition and/or a parameter value that leads to chaotic attractors, there are initial conditions and/or parameter values arbitrarily nearby that lead to nonchaotic attractors. This indicates the occurrence of an extreme type of fractal structure in both phase space and parameter space. A scaling exponent used to characterize extreme sensitive dependence on initial conditions and parameters is determined to be near zero in both phase space and parameter space. Accordingly, there is a significant probability of error in numerical computations intended to determine asymptotic attractors, regardless of the precision with which initial conditions or parameters are specified. Consequently, fundamental statistical properties of asymptotic attractors cannot be computed reliably for particular parameter values and initial conditions.

KW - FRACTAL BASIN BOUNDARIES

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KW - STRANGE ATTRACTOR

KW - INTERMITTENCY

KW - TRANSITION

KW - DIMENSION

KW - BEHAVIOR

KW - SURFACE

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JO - Physica. D, Nonlinear Phenomena

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