Upper bound for the time derivative of entropy for a dynamical system driven by coloured cross-correlated white noises

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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Effect of time delay on the upper bound of the time derivative of information entropy in a stochastic dynamical system

Chinese Physics B ◽

10.1088/1674-1056/20/11/110501 ◽

2011 ◽

Vol 20 (11) ◽

pp. 110501

Author(s):

Min-Min Zhang ◽

Can-Jun Wang ◽

Dong-Cheng Mei

Keyword(s):

Dynamical System ◽

Time Delay ◽

Information Entropy ◽

Upper Bound ◽

Time Derivative ◽

Stochastic Dynamical System

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Composite hierarchical anti-disturbance control for stochastic systems with multiple disturbances

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331217695385 ◽

2017 ◽

Vol 40 (6) ◽

pp. 1950-1955 ◽

Cited By ~ 1

Author(s):

Shixiang Sun ◽

Xinjiang Wei ◽

Huifeng Zhang

Keyword(s):

Disturbance Observer ◽

Closed Loop ◽

Stochastic Systems ◽

Time Derivative ◽

Closed Loop System ◽

Stochastic Disturbance ◽

Multiple Disturbances ◽

Control Scheme ◽

Bounded Disturbance ◽

White Noises

A class of stochastic systems with multiple disturbances, which includes white noises and disturbances whose time derivative is bounded, is considered in this paper. To estimate the unknown bounded disturbance, a stochastic disturbance observer is proposed. Based on the observer, a disturbance observer-based disturbance control scheme is constructed such that the composite closed-loop system is asymptotically bounded. Finally, a simulation example is given to demonstrate the feasibility and effectiveness of the proposed scheme.

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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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Upper Bound of Time Derivative of Information Entropy in Non-Markovian Stochastic Process

Czechoslovak Journal of Physics ◽

10.1023/b:cjop.0000020578.20658.e4 ◽

2004 ◽

Vol 54 (4) ◽

pp. 389-396

Author(s):

Pradip Majee ◽

Bidhan Chandra Bag

Keyword(s):

Stochastic Process ◽

Information Entropy ◽

Upper Bound ◽

Time Derivative

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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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Complex Dynamics of Credit Risk Contagion with Time-Delay and Correlated Noises

Abstract and Applied Analysis ◽

10.1155/2014/456764 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 2

Author(s):

Tingqiang Chen ◽

Xindan Li ◽

Jianmin He

Keyword(s):

Dynamical System ◽

Time Delay ◽

Probability Distribution ◽

Credit Risk ◽

Resistance Coefficient ◽

Stationary Probability ◽

Stationary Probability Distribution ◽

Credit Risk Contagion ◽

Nonlinear Resistance ◽

White Noises

The stochastic time-delayed system of credit risk contagion driven by correlated Gaussian white noises is investigated. Novikov’s theorem, the time-delay approximation, the path-integral approach, and first-order perturbation theory are used to derive time-delayed Fokker-Planck model and the stationary probability distribution function of the dynamical system of credit risk contagion in the financial market. Using the method of numerical simulation, the Hopf bifurcation and chaotic behaviors of credit risk contagion are analyzed when time-delay and nonlinear resistance coefficient are varied and the effects of time-delay, nonlinear resistance and the intensity and the correlated degree of correlated Gaussian white noises on the stationary probability distribution of credit risk contagion are investigated. It is found that, as the infectious scale of credit risk and the wavy frequency of credit risk contagion are increased, the stability of the system of credit risk contagion is reduced, the dynamical system of credit risk contagion gives rise to chaotic phenomena, and the chaotic area increases gradually with the increase in time-delay. The nonlinear resistance only influences the infectious scale and range of credit risk, which is reduced when the nonlinear resistance coefficient increases. In addition, the curve of the stationary probability distribution is monotone decreasing with the increase in parameters value of time-delay, nonlinear resistance, and the intensity and the correlated degree of correlated Gaussian white noises.

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