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Identification of generic stable dynamical systems taking a nonlinear differential approach

This work was supported in part by a grant from the Institute for Research in Fundamental Sciences (IPM) [No. 95510037].
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  • Identifying new stable dynamical systems, such as generic stable mechanical or electrical control systems, requires questing for the desired systems parameters that introduce such systems. In this paper, a systematic approach to construct generic stable dynamical systems is proposed. In fact, our approach is based on a simple identification method in which we intervene directly with the dynamics of our system by considering a continuous $1$-parameter family of system parameters, being parametrized by a positive real variable $\ell$, and then identify the desired parameters that introduce a generic stable dynamical system by analyzing the solutions of a special system of nonlinear functional-differential equations associated with the $\ell$-varying parameters. We have also investigated the reliability and capability of our proposed approach.

    To illustrate the utility of our result and as some applications of the nonlinear differential approach proposed in this paper, we conclude with considering a class of coupled spring-mass-dashpot systems, as well as the compartmental systems - the latter of which provide a mathematical model for many complex biological and physical processes having several distinct but interacting phases.

    Mathematics Subject Classification: Primary: 34D20, 37C75; Secondary: 65L03, 93D05.


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  • Figure 1.  Schematic of a coupled spring-mass-dashpot system

    Figure 2.  Schematic of an open compartmental system

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