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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 |
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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 UB(t) of the time derivative of the information entropy. The results show that there is a critical value of $\tau$ (delay time), and UB(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 UB(t)-$\lambda$ plot, where $\lambda$ denotes the degree of the correlation between the two noises.
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Received: 22 March 2011
Revised: 05 May 2011
Accepted manuscript online:
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PACS:
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05.45.-a
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(Nonlinear dynamics and chaos)
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05.40.Ca
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(Noise)
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05.70.Ln
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(Nonequilibrium and irreversible thermodynamics)
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05.20.-y
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(Classical statistical mechanics)
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| Fund: 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). |
Cite this article:
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 2011 Chin. Phys. B 20 110501
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