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This Concept Map, created with IHMC CmapTools, has information related to: c1. Lyapunov Exponents, A Lyapunov exponent is a number that reflects the RATE of divergence or convergence, AVERAGED over the entire attractor, of two neighboring phase space trajectories. ???? Its value can be positive, zero, or negative., A negative Lyapunov exponent indicates an average convergence of trajectories. ???? Convergence, and hence negative Lyapunov exponents, typifies non-chaotic attractors., Its value can be positive, zero, or negative. ???? A negative Lyapunov exponent indicates an average convergence of trajectories., A Lyapunov exponent is a number that reflects the RATE of divergence or convergence, AVERAGED over the entire attractor, of two neighboring phase space trajectories. ???? A positive Lyapunov exponent is one of the most important indicators of chaos., Convergence, and hence negative Lyapunov exponents, typifies non-chaotic attractors. ???? The separations must plot as a straight line with the trajectory gap on the ordinate (log scale) and time on the abscissa (arithmetic scale)., Positive exponents result from trajectory divergence, and appear only in the chaotic domain. ???? The separations must plot as a straight line with the trajectory gap on the ordinate (log scale) and time on the abscissa (arithmetic scale)., A positive Lyapunov exponent is one of the most important indicators of chaos. ???? A positive Lyapunov exponent measures or quantifies sensitive dependence on initial conditions by showing the average rate at which two close points separate over time., Positive exponents result from trajectory divergence, and appear only in the chaotic domain. ???? Divergence and hence at least one positive Lyapunov exponent usually occurs only on chaotic attractors., c1. Lyapunov Exponents ???? A Lyapunov exponent is a number that reflects the RATE of divergence or convergence, AVERAGED over the entire attractor, of two neighboring phase space trajectories., A Lyapunov exponent is a number that describes the dynamics of trajectory evolution. ???? A Lyapunov exponent is a number that reflects the RATE of divergence or convergence, AVERAGED over the entire attractor, of two neighboring phase space trajectories., A Lyapunov exponent is a number that describes the dynamics of trajectory evolution. ???? A positive Lyapunov exponent is one of the most important indicators of chaos., Its value can be positive, zero, or negative. ???? A positive exponent indicates a divergence., A positive Lyapunov exponent measures or quantifies sensitive dependence on initial conditions by showing the average rate at which two close points separate over time. ???? Positive exponents result from trajectory divergence, and appear only in the chaotic domain., A positive Lyapunov exponent is one of the most important indicators of chaos. ???? A positive exponent indicates a divergence., Convergence, and hence negative Lyapunov exponents, typifies non-chaotic attractors. ???? Convergence can also take place on chaotic attractors., c1. Lyapunov Exponents ???? A Lyapunov exponent is a number that describes the dynamics of trajectory evolution.