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

doi:10.1088/1674-1056/20/11/110501

中国物理B ›› 2011, Vol. 20 ›› Issue (11): 110501-110501.doi: 10.1088/1674-1056/20/11/110501

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

张敏敏¹, 梅冬成¹, 王参军²

(1)Department of Physics, Yunnan University, Kunming 650091, China; (2)Nonlinear Research Institute, Baoji University of Arts and Sciences, Baoji 721016, China

收稿日期:2011-03-22 修回日期:2011-05-05 出版日期:2011-11-15 发布日期:2011-11-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 10865006), the Science Foundation of Yunnan University, China (Grant No. 2009A01z), the Natural Science Foundation of Shaanxi Province, China (Grant No. 2010JQ1014), and the Science Foundation of Baoji University of Science and Arts of China (Grant No. ZK0954).

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

Zhang Min-Min(张敏敏)^a), Wang Can-Jun(王参军)^b), and Mei Dong-Cheng(梅冬成)^a)†

^a Department of Physics, Yunnan University, Kunming 650091, China; ^b Nonlinear Research Institute, Baoji University of Arts and Sciences, Baoji 721016, China

Received:2011-03-22 Revised:2011-05-05 Online:2011-11-15 Published:2011-11-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 10865006), the Science Foundation of Yunnan University, China (Grant No. 2009A01z), the Natural Science Foundation of Shaanxi Province, China (Grant No. 2010JQ1014), and the Science Foundation of Baoji University of Science and Arts of China (Grant No. ZK0954).

摘要/Abstract

摘要： The effects of the time delay on the upper bound of the time derivative of information entropy are investigated in a time-delayed dynamical system driven by correlated noise. Using the Markov approximation of the stochastic delay differential equations and the Schwartz inequality principle, we obtain an analytical expression for the upper bound U_B(t) of the time derivative of the information entropy. The results show that there is a critical value of τ (delay time), and U_B(t) presents opposite behaviours on difference sides of the critical value. For the case of the weak additive noise, τ can induce a reentrance transition. Delay time τ also causes a reversal behaviour in U_B(t)-λ plot, where λ denotes the degree of the correlation between the two noises.

关键词: information entropy, upper bound, time delay, noise

Abstract: The effects of the time delay on the upper bound of the time derivative of information entropy are investigated in a time-delayed dynamical system driven by correlated noise. Using the Markov approximation of the stochastic delay differential equations and the Schwartz inequality principle, we obtain an analytical expression for the upper bound U_B(t) of the time derivative of the information entropy. The results show that there is a critical value of $\tau$ (delay time), and U_B(t) presents opposite behaviours on difference sides of the critical value. For the case of the weak additive noise, $\tau$ can induce a reentrance transition. Delay time $\tau$ also causes a reversal behaviour in U_B(t)-$\lambda$ plot, where $\lambda$ denotes the degree of the correlation between the two noises.

Key words: information entropy, upper bound, time delay, noise

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

05.40.Ca (Noise) 05.70.Ln (Nonequilibrium and irreversible thermodynamics) 05.20.-y (Classical statistical mechanics)

张敏敏, 王参军, 梅冬成. Effect of time delay on the upper bound of the time derivative of information entropy in a stochastic dynamical system[J]. 中国物理B, 2011, 20(11): 110501-110501.

Zhang Min-Min(张敏敏), Wang Can-Jun(王参军), and Mei Dong-Cheng(梅冬成) . Effect of time delay on the upper bound of the time derivative of information entropy in a stochastic dynamical system[J]. Chin. Phys. B, 2011, 20(11): 110501-110501.

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

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

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