Coloured thermal noise-driven dynamical system: upper bound of time derivative of information entropy

The upper bound UB(t) of the time derivative of entropy for a dynamical system driven by both additive colored noise and multiplicative colored noise with colored cross-correlation is investigated. Based on the Fokker–Planck equation, the effects of the parameters on UB(t) are analyzed. The results show that: (i) α (the multiplicative noise intensity), D (the additive noise intensity) and τ2 (the correlation time of the additive noise) always enhance UB (t) monotonically; (ii) λ (the intensity of the cross-correlation between the multiplicative noise and the additive noise), τ1 (the correlation time of the multiplicative noise), τ3 (the correlation time of the cross-correlation) and γ (the dissipative constant) all possess a minimum, i.e., UB (t) decreases for small values and increases for large values.

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Upper bound of time derivative of entropy for a dynamical system driven by quasimonochromatic noise

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2010.04.013 ◽

2011 ◽

Vol 16 (1) ◽

pp. 522-527 ◽

Cited By ~ 6

Author(s):

Yongfeng Guo ◽

Wei Xu ◽

Hongtao Liu ◽

Dongxi Li ◽

Liang Wang

Keyword(s):

Dynamical System ◽

Upper Bound ◽

Time Derivative

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New Stabilization for Dynamical System with Two Additive Time-Varying Delays

The Scientific World JOURNAL ◽

10.1155/2014/315817 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Lianglin Xiong ◽

Fan Yang ◽

Xiaozhou Chen

Keyword(s):

Dynamical System ◽

Upper Bound ◽

Lyapunov Functional ◽

Time Varying ◽

The Novel ◽

Decomposition Technique ◽

Delay Dependent ◽

Delay Decomposition ◽

Reciprocally Convex Approach

This paper provides a new delay-dependent stabilization criterion for systems with two additive time-varying delays. The novel functional is constructed, a tighter upper bound of the derivative of the Lyapunov functional is obtained. These results have advantages over some existing ones because the combination of the delay decomposition technique and the reciprocally convex approach. Two examples are provided to demonstrate the less conservatism and effectiveness of the results in this paper.

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Bekenstein–Hawking entropy for discrete dynamical systems on sites

Modern Physics Letters A ◽

10.1142/s0217732319502651 ◽

2019 ◽

Vol 34 (32) ◽

pp. 1950265

Author(s):

Sh. Najmizadeh ◽

M. Toomanian ◽

M. R. Molaei ◽

T. Nasirzade

Keyword(s):

Dynamical System ◽

Dynamical Systems ◽

Upper Bound ◽

Discrete Dynamical System ◽

Discrete Dynamical Systems ◽

New Class ◽

A Site

In this paper, we extend the notion of Bekenstein–Hawking entropy for a cover of a site. We deduce a new class of discrete dynamical system on a site and we introduce the Bekenstein–Hawking entropy for each member of it. We present an upper bound for the Bekenstein–Hawking entropy of the iterations of a dynamical system. We define a conjugate relation on the set of dynamical systems on a site and we prove that the Bekenstein–Hawking entropy preserves under this relation. We also prove that the twistor correspondence preserves the Bekenstein–Hawking entropy.

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