Mathematical analysis of the Wiener processes with time-delayed feedback
Source abstract
Abstract
It is known that time delays generally make a system unstable. However, it is numerically observed that the diffusion coefficients of the Wiener processes with time-delayed feedback decrease while increasing the time delay τ. In particular, the decay of the diffusion coefficients with the form (11+τ)2 has been confirmed by numerical simulations [Ando et al., Phys. Rev. E 96, 012148 (2017)]. In this paper, we present two analytical derivations for the relation (11+τ)2 by dynamical system approaches using the Laplace transform and stochastic differential equations.
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Research context
OpenAlex topics: Nonlinear Dynamics and Pattern Formation · stochastic dynamics and bifurcation · Neural dynamics and brain function
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Affiliations
Faculty of Economics, Rissho University 1 , 4-2-16 Osaki, Shinagawa-ku, Tokyo 141-8602, Japan
Graduate School of Social Science, Tokyo Metropolitan University 2 , 1-4-1 Marunouchi, Chiyoda-ku, Tokyo 100-0005, Japan
Faculty of Engineering, Information and Systems, University of Tsukuba 3 , 1-1-1 Ten-noudai, Tsukuba 305-8573, Japan
Research Institute for Mathematical Sciences, Kyoto University 4 , Kyoto 606-8502, Japan
Funding
Japan Society for the Promotion of Science
References (11)
Show source-provided references
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