Dynamical System
المؤلف:
Aoki, N. and Hiraide, K
المصدر:
Topological Theory of Dynamical Systems. Amsterdam, Netherlands: North-Holland, 1994.
الجزء والصفحة:
...
7-10-2021
1297
Dynamical System
A means of describing how one state develops into another state over the course of time. Technically, a dynamical system is a smooth action of the reals or the integers on another object (usually a manifold). When the reals are acting, the system is called a continuous dynamical system, and when the integers are acting, the system is called a discrete dynamical system. If 
is any continuous function, then the evolution of a variable 
can be given by the formula
 |
(1)
|
This equation can also be viewed as a difference equation
 |
(2)
|
so defining
 |
(3)
|
gives
 |
(4)
|
which can be read "as 
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.
Jordan, D. W. and Smith, P. Nonlinear Ordinary Differential Equations: An Introduction to Dynamical Systems, 3rd ed. Oxford, England: Oxford University Press, 1999.
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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