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In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a set, without the need of a smooth space-time structure defined on it.
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists since most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems.
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References
- 1 2 Mathematical Association of America, Chauvenet Prize recipients
- 1 2 Joseph P. LaSalle Guggenheim Fellowship, 1975
- 1 2 J. P. LaSalle on the Mathematics Genealogy Project
- 1 2 3 4 5 SIAM J. Control Optim., 21(6), vii–ix. In Memoriam
- ↑ LaSalle, J. P. (Dec 1960). "Some extensions of Liapunov's second method" (PDF). IRE Transactions on Circuit Theory . IEEE. 7 (4): 520–527. doi:10.1109/TCT.1960.1086720. Archived from the original (PDF) on 2019-04-30. Retrieved 2016-07-04.
- ↑ Presidents of SIAM
- ↑ Journal of Differential Equations Editorial Board
- ↑ Center for Dynamical Systems at Brown University
- ↑ LaSalle, Joseph P.; Hale, Jack K. (July 1963). "Differential Equations: Linearity vs. Nonlinearity" (PDF). SIAM Review . SIAM. 5 (3): 249–272. Bibcode:1963SIAMR...5..249H. doi:10.1137/1005068 . Retrieved 2016-07-04.
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