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Finding, Stabilizing, and Verifying Cycles of Nonlinear Dynamical Systems. (arXiv:1712.06035v1 [math.DS])
来源于:arXiv
We present a new solution for fundamental problems in nonlinear dynamical
systems: finding, verifying, and stabilizing cycles. The solution we propose
consists of a new control method based on mixing previous states of the system
(or the functions of these states). This approach allows us to locally
stabilize and to find a priori unknown cycles of a given length. Our method
generalizes and improves on the existing one dimensional space solutions to
multi-dimensional space while using the geometric complex functions theory
rather than a linear algebra approach. Several numerical examples are
considered. All statements and formulas are given in final form. The formulas
derivation and reasoning may be found in the cited references. The article
focuses on practical applications of methods and algorithms. 查看全文>>