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

Wang, Can-Jun; Mei, Dong-Cheng

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

Cited by 2 publications

(2 citation statements)

References 26 publications

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“…Furthermore, considering that carbon emission and carbon absorption are not only related to the current time, but also to the past time, we can use the delayed differential equation model to describe the phenomenon of the dynamic system of carbon emission and carbon absorption more truly and accurately. There is a lot of research work on delayed differential equations in many fields, such as biology, medicine, physics, and so on [14][15][16][17][18]. At present, there are few research achievements in describing carbon emission and carbon absorption model by using delayed differential equations, so the purpose of this paper is to use delayed differential equations to describe carbon emission and carbon absorption model.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling and Stability Analysis of a Delayed Carbon Absorption-Emission Model Associated with China’s Adjustment of Industrial Structure

2022

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Global warming has brought about enormous damage, therefore, some scholars have begun to conduct in-depth research on peak carbon dioxide emissions and carbon neutrality. In this paper, based on the background of China’s upgrading industrial structure and energy structure, we establish a delayed two-dimensional differential equation model associated with China’s adjustment of industrial structure. Firstly, we analyze the existence of the equilibrium for the model. We also analyze the characteristic roots of the characteristic equation at each equilibrium point for the model, then, we analyze the stability of the equilibrium point for the model according to the characteristic root, and discuss the existence of Hopf bifurcation of the system by using bifurcation theory. Secondly, we derive the normal form of Hopf bifurcation by using the multiple time scales method. Then, through the official real data, we present the range of some parameters in the model, and determine a set of parameters by reasonable analysis. The validity of the theoretical results is verified by numerical simulations. Finally, we use the real data to forecast the time of peak carbon dioxide emissions and carbon neutralization. Eventually, we put forward some suggestions based on the current situation of carbon emission and absorption in China, such as planting trees to increase the growth rate of carbon absorption, deepening industrial reform and optimizing energy structure to reduce carbon emissions.

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Section: Introductionmentioning

confidence: 99%

Mathematical Modeling and Stability Analysis of a Delayed Carbon Absorption-Emission Model Associated with China’s Adjustment of Industrial Structure

2022

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“…Time delay is ubiquitous in most physical and biological systems, arising from finite propagation speeds of signals, which has been widely studied in the context of coupled limit cycle oscillator systems, [1][2][3][4] for example, the semiconductor lasers, [5] neuronal networks, [6][7][8] etc.…”

Section: Introductionmentioning

confidence: 99%

Effects of time delays in a mathematical bone model

2017

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In this paper we propose a mathematical model of bone remodeling with time delays of both osteoclast-derived paracrine signaling of tumor and tumor-derived paracrine signaling of osteoclast. The effects of time delays on the growth of tumor cells and bone system are studied in multiple myeloma-induced bone disease. In the case of small osteoclast-derived paracrine signaling, it is found that the growth of tumor cells slows down, the oscillation period of the ratio of osteoclasts to osteoblasts is extended with increasing time delay, and there is a competition between the delay and osteoclast-derived paracrine signaling. In the case of large tumor-derived paracrine signaling, the tumor-derived paracrine signaling can induce a more significant decline in tumor growth for long time delay, and thus slowing down the progression of bone disease. There is an optimal coupling between the tumor-derived paracrine signaling of osteoclasts and time delay during the progressions of bone diseases, which suppresses the tumor growth and the regression of bone disease.

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

Abstract: Effect of time delay on the upper bound of the time derivative of information entropy in a stochastic dynamical system *Zhang Min-Min( ) a) , Wang Can-Jun( ) b) , and Mei Dong-Cheng( ) a) †

Cited by 2 publications

References 26 publications

Mathematical Modeling and Stability Analysis of a Delayed Carbon Absorption-Emission Model Associated with China’s Adjustment of Industrial Structure

Mathematical Modeling and Stability Analysis of a Delayed Carbon Absorption-Emission Model Associated with China’s Adjustment of Industrial Structure

Effects of time delays in a mathematical bone model

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