| 释义 |
Dynamical SystemA means of describing how one state develops into another state over the course of time. Technically, a dynamical system is asmooth action of the reals or the Integers on another object (usually a Manifold). When the realsare acting, the system is called a continuous dynamical system, and when the Integers are acting, thesystem is called a discrete dynamical system. If  is any Continuous Function, then the evolution of a variable  can be given by the formula
 | (1) |
 | (2) |
 | (3) |
 | (4) |
 changes by 1 unit, changes by  .'' This is the discrete analog of the Differential Equation
 | (5) |
References
Aoki, N. and Hiraide, K. Topological Theory of Dynamical Systems. Amsterdam, Netherlands: North-Holland, 1994.Golubitsky, M. Introduction to Applied Nonlinear Dynamical Systems and Chaos. New York: Springer-Verlag, 1997. Guckenheimer, J. and Holmes, P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, 3rd ed. New York: Springer-Verlag, 1997. Lichtenberg, A. and Lieberman, M. Regular and Stochastic Motion, 2nd ed. New York: Springer-Verlag, 1994. Ott, E. Chaos in Dynamical Systems. New York: Cambridge University Press, 1993. Rasband, S. N. Chaotic Dynamics of Nonlinear Systems. New York: Wiley, 1990. Strogatz, S. H. Nonlinear Dynamics and Chaos, with Applications to Physics, Biology, Chemistry, and Engineering. Reading, MA: Addison-Wesley, 1994. Tabor, M. Chaos and Integrability in Nonlinear Dynamics: An Introduction. New York: Wiley, 1989.
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