Multiple Time Delays Induced Dynamics of p53 Gene Regulatory Network

2021 ◽  
Vol 31 (15) ◽  
Author(s):  
Yuanhong Bi ◽  
Yanan Li ◽  
Jianmin Hou ◽  
Quansheng Liu
Keyword(s):  
Time Delay ◽  
Equilibrium Point ◽  
Regulatory Network ◽  
Time Delays ◽  
P53 Gene ◽  
Positive Equilibrium ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
Gene Regulatory ◽  
Positive Equilibrium Point

p53 dynamics plays an important role in determining cell arrest or apoptosis upon DNA damage response. In this paper, based on a p53 gene regulatory network composed of its core regulator ATM, Mdm2 and Wip1, the effect of multiple time delays in transcription and translation of Mdm2 and Wip1 gene expression on p53 dynamics are investigated through theoretical and numerical analyses. The stability of the positive equilibrium point and the existence of Hopf bifurcation are demonstrated through analyzing the associated characteristic equation of the corresponding linearized system in five cases. Detailed numerical simulations and bifurcation analyses are performed to support the theoretical results. The results show that with the increase of a time delay, the positive equilibrium point becomes unstable, and the p53 dynamics presents an oscillating state. These results reveal that time delay has a significant impact on p53 dynamics and may provide a useful insight into developing anti-cancer therapy.

Impacts of Multiple Time Delays on a Gene Regulatory Network Mediated by Small Noncoding RNA

2020 ◽  
Vol 30 (05) ◽  
pp. 2050069
Author(s):  
Ming Liu ◽  
Fanwei Meng ◽  
Dongpo Hu
Keyword(s):  
Hopf Bifurcation ◽  
Gene Regulatory Network ◽  
Regulatory Network ◽  
Time Delays ◽  
Noncoding Rna ◽  
Multiple Time ◽  
Normal Form Theory ◽  
Small Noncoding Rna ◽  
Multiple Time Delays ◽  
Gene Regulatory

In this paper, the impacts of multiple time delays on a gene regulatory network mediated by small noncoding RNA is studied. By analyzing the associated characteristic equation of the corresponding linearized system, the asymptotic stability of the positive equilibrium is investigated and Hopf bifurcation is demonstrated. Furthermore, the explicit formulae for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are given by the center manifold theorem and the normal form theory for functional differential equations. Finally, some numerical simulations are demonstrated for supporting the theoretical results.

scholarly journals Delayed dynamical systems: networks, chimeras and reservoir computing

2019 ◽  
Vol 377 (2153) ◽  
pp. 20180123 ◽  
Author(s):  
Joseph D. Hart ◽  
Laurent Larger ◽  
Thomas E. Murphy ◽  
Rajarshi Roy
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
System Dynamics ◽  
Coupled Oscillators ◽  
Time Delays ◽  
Delay Systems ◽  
Multiple Time ◽  
Reservoir Computing ◽  
Multiple Time Delays ◽  
Network Topologies

We present a systematic approach to reveal the correspondence between time delay dynamics and networks of coupled oscillators. After early demonstrations of the usefulness of spatio-temporal representations of time-delay system dynamics, extensive research on optoelectronic feedback loops has revealed their immense potential for realizing complex system dynamics such as chimeras in rings of coupled oscillators and applications to reservoir computing. Delayed dynamical systems have been enriched in recent years through the application of digital signal processing techniques. Very recently, we have showed that one can significantly extend the capabilities and implement networks with arbitrary topologies through the use of field programmable gate arrays. This architecture allows the design of appropriate filters and multiple time delays, and greatly extends the possibilities for exploring synchronization patterns in arbitrary network topologies. This has enabled us to explore complex dynamics on networks with nodes that can be perfectly identical, introduce parameter heterogeneities and multiple time delays, as well as change network topologies to control the formation and evolution of patterns of synchrony. This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.

scholarly journals Dynamical Models For Prices With Distributed Delays

2015 ◽  
Vol 8 (1) ◽  
pp. 91-102
Author(s):  
Gabriela Mircea ◽  
Mihaela Neamţu ◽  
Laura Mariana Cismaş
Keyword(s):  
Time Delay ◽  
Equilibrium Point ◽  
Supply And Demand ◽  
Positive Equilibrium ◽  
Asymptotically Stable ◽  
Dynamical Models ◽  
Demand Functions ◽  
Distributed Time Delay ◽  
Commodity Demand ◽  
Positive Equilibrium Point

Abstract In the present paper we study some models for the price dynamics of a single commodity market. The quantities of supplied and demanded are regarded as a function of time. Nonlinearities in both supply and demand functions are considered. The inventory and the level of inventory are taken into consideration. Due to the fact that the consumer behavior affects commodity demand, and the behavior is influenced not only by the instantaneous price, but also by the weighted past prices, the distributed time delay is introduced. The following kernels are taken into consideration: demand price weak kernel and demand price Dirac kernel. Only one positive equilibrium point is found and its stability analysis is presented. When the demand price kernel is weak, under some conditions of the parameters, the equilibrium point is locally asymptotically stable. When the demand price kernel is Dirac, the existence of the local oscillations is investigated. A change in local stability of the equilibrium point, from stable to unstable, implies a Hopf bifurcation. A family of periodic orbits bifurcates from the positive equilibrium point when the time delay passes through a critical value. The last part contains some numerical simulations to illustrate the effectiveness of our results and conclusions.

scholarly journals The role of time delays in P53 gene regulatory network stimulated by growth factor

2020 ◽  
Vol 17 (4) ◽  
pp. 3794-3835
Author(s):  
Changyong Dai ◽  
◽  
Haihong Liu ◽  
Fang Yan ◽  
Keyword(s):  
Growth Factor ◽  
Gene Regulatory Network ◽  
Regulatory Network ◽  
Time Delays ◽  
P53 Gene ◽  
Gene Regulatory

Conversion of SISO processes with multiple time-delays to single time-delay processes

2018 ◽  
Vol 65 ◽  
pp. 84-90 ◽  
Author(s):  
Xiaoli Luan ◽  
Qiang Chen ◽  
Pedro Albertos ◽  
Fei Liu
Keyword(s):  
Time Delay ◽  
Time Delays ◽  
Multiple Time ◽  
Single Time ◽  
Multiple Time Delays

scholarly journals Combination Synchronization of Three Different Fractional-Order Delayed Chaotic Systems

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Bo Li ◽  
Xiaobing Zhou ◽  
Yun Wang
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Time Delays ◽  
Chaotic Systems ◽  
Multiple Time ◽  
Engineering Systems ◽  
Fractional Order Systems ◽  
Combination Synchronization ◽  
Multiple Time Delays ◽  
Practical Engineering

Time delay is a frequently encountered phenomenon in some practical engineering systems and introducing time delay into a system can enrich its dynamic characteristics. There has been a plenty of interesting results on fractional-order chaotic systems or integer-order delayed chaotic systems, but the problem of synchronization of fractional-order chaotic systems with time delays is in the primary stage. Combination synchronization of three different fractional-order delayed chaotic systems is investigated in this paper. It is an extension of combination synchronization of delayed chaotic systems or combination synchronization of fractional-order chaotic systems. With the help of stability theory of linear fractional-order systems with multiple time delays, we design controllers to achieve combination synchronization of three different fractional-order delayed chaotic systems. In addition, numerical simulations have been performed to demonstrate and verify the theoretical analysis.

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