2001/01/21 by Alexander N. Jourjine, Jourjine, Alexander N.
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Gene Regulatory Network Analysis #Neural Networks Stability and Synchronization #Nonlinear Dynamics and Pattern Formation #nlin.AO #nlin.CD
paper · pdf · doi:10.48550/arxiv.nlin/0101038
This paper is being submitted to the Journal of Nonlinear Sciences. This is a .tex file generated with SciWord 3.0. 17 pages. No figures. 01.03.17. Contact E-mail corrected, address added Contact address and e-mail updated
openalex publication_date 2001/01/21 · arxiv created 2001/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial condition of a linear delay-differential system. It is further shown that the initial condition can be extended to a periodic solution of the delay-differential system if an appropriate choice of its parameters is made. As a result, any finite set of trajectories of a nonlinear dynamical system can be modeled with arbitrarily small error via a set of periodic solutions of a linear delay-differential equation. These results can be extended to some non-linear delay differential systems. One application of the method is for modeling memory and perception.