scholarly journals Delay-Induced Self-Organization Dynamics in a Prey-Predator Network with Diffusion

2021 ◽  
Author(s):  
Qing Hu ◽  
Jianwei Shen
Keyword(s):  
Time Delays ◽  
Random Network ◽  
Turing Instability ◽  
Self Organization ◽  
Network System ◽  
Turing Pattern ◽  
Network Connection ◽  
Pattern Dynamics ◽  
Connection Probability ◽  
The Stability

Abstract Time delays can induce the loss of stability and degradation of performance. In this paper, the pattern dynamics of a prey-predator network with diffusion and delay are investigated, where the inhomogeneous distribution of species in space can be viewed as a random network, and delay can affect the stability of the network system. Our results show that time delay can induce the emergence of Hopf and Turing bifurcations, which are independent of the network, and the conditions of bifurcation are derived by linear stability analysis. Moreover, we find that the Turing pattern can be related to the network connection probability. The Turing instability region involving delay and network connection probability is obtained. Finally, the numerical simulation verifies our results.

scholarly journals Turing Instability of Brusselator in the Reaction-Diffusion Network

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Yansu Ji ◽  
Jianwei Shen
Keyword(s):  
Diffusion Coefficient ◽  
Random Network ◽  
Reaction Diffusion ◽  
Turing Instability ◽  
Spontaneous Generation ◽  
Brusselator Model ◽  
Network Connection ◽  
Pattern Dynamics ◽  
Connection Probability ◽  
And Diffusion

Turing instability constitutes a universal paradigm for the spontaneous generation of spatially organized patterns, especially in a chemical reaction. In this paper, we investigated the pattern dynamics of Brusselator from the view of complex networks and considered the interaction between diffusion and reaction in the random network. After a detailed theoretical analysis, we obtained the approximate instability region about the diffusion coefficient and the connection probability of the random network. In the meantime, we also obtained the critical condition of Turing instability in the network-organized system and found that how the network connection probability and diffusion coefficient affect the reaction-diffusion system of the Brusselator model. In the end, the reason for arising of Turing instability in the Brusselator with the random network was explained. Numerical simulation verified the theoretical results.

scholarly journals Qualitative Dynamics and Pattern Formation of COVID-19 in the Modified SIR Model

2021 ◽  
Author(s):  
Qianqian Zheng ◽  
Vikas Pandey ◽  
Jianwei Shen ◽  
Yong Xu ◽  
Linan Guan
Keyword(s):  
Infectious Diseases ◽  
Critical Role ◽  
Turing Instability ◽  
Sir Model ◽  
Vital Role ◽  
Network Connection ◽  
Novel Approach ◽  
System Method ◽  
The Stability ◽  
Random Diffusion

Abstract SIR (susceptible-infective-recovery) model is a widely investigated model to explain the time evolution of infectious diseases. Outbreak of infectious diseases is affected by diffusion of infected, which is true especially in COVID-19 outbreak. Therefore, it is imperative to construct a diffusion network in the model for spatial consideration; However, the inclusion of a diffusion network is seldom considered for the studies. In this work, we first modified the SIR model for COVID-19 and then performed its stability and bifurcation analysis in qualitative research. Based on our analysis, we propose some of the advice to mitigate the spread of COVID-19. Then, a random diffusion network is constructed, which shows its vital role in the Turing instability and bifurcation. We noticed that the stability of network-organized SIR could be determined by the maximum of eigenvalues of the network matrix. The maximum of eigenvalues of the network matrix is proportional to network connection rate and infection rate of the network. Therefore, these two rates play a critical role in Turing instability. We perform the numerical simulations to verify the analytical results. We try to explain the spread mechanism of infectious diseases and provide some feasible strategies based on our analysis of these two models. Also, the reduced system method for a network-organized system is proposed, which is a novel approach to investigate the complex system.

scholarly journals The Dynamics of a Diffusive Nutrient-Algae Model Based upon the Sanyang Wetland

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Yi Wang ◽  
Min Zhao ◽  
Chuanjun Dai ◽  
Yunli Deng
Keyword(s):  
Spatial Distribution ◽  
Aquatic Ecosystems ◽  
Local Stability ◽  
Turing Instability ◽  
Theoretical Studies ◽  
Turing Pattern ◽  
Input Rate ◽  
Nutrient Input ◽  
The Stability ◽  
Positivity And Boundedness

The stability and spatiotemporal dynamics of a diffusive nutrient-algae model are investigated mathematically and numerically. Mathematical theoretical studies have considered the positivity and boundedness of the solution and the existence, local stability, and global stability of equilibria. Turing instability has also been studied. Furthermore, a series of numerical simulations was performed and a complex Turing pattern found. These results indicate that the nutrient input rate has an important influence on the density and spatial distribution of algae populations. This may help us to obtain a better understanding of the interactions of nutrient and algae and to investigate plankton dynamics in aquatic ecosystems.

scholarly journals Dynamical study of infochemical influences on tropic interaction of diffusive plankton system

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
Satish Kumar Tiwari ◽  
Ravikant Singh ◽  
Nilesh Kumar Thakur
Keyword(s):  
Dimethyl Sulfide ◽  
Algal Bloom ◽  
Turing Instability ◽  
Model System ◽  
Ode Model ◽  
Estuarine Ecosystem ◽  
Dynamical Study ◽  
Oscillatory Dynamics ◽  
The Stability ◽  
Microzooplankton Grazing

AbstractWe propose a model for tropic interaction among the infochemical-producing phytoplankton and non-info chemical-producing phytoplankton and microzooplankton. Volatile information-conveying chemicals (infochemicals) released by phytoplankton play an important role in the food webs of marine ecosystems. Microzooplankton is an ecologically important grazer of phytoplankton for coexistence of a large number of phytoplankton species. Here, we discuss how information transferred by dimethyl sulfide shapes the interaction of phytoplankton. Phytoplankton deterrents may lead to propagation of IPP bloom. The interaction between IPP and microzooplankton follows the Beddington–DeAngelis-type functional response. Analytically, we discuss boundedness, stability and Turing instability of the model system. We perform numerical simulation for temporal (ODE model) as well as a spatial model system. Our numerical investigation shows that microzooplankton grazing refuse of IPP leads to oscillatory dynamics. Increasing diffusion coefficient of microzooplankton shows Turing instability. Time evolution also plays an important role in the stability of system dynamics. The results obtained in this paper are useful to understand the dominance of algal bloom in coastal and estuarine ecosystem.

scholarly journals Optimal harvesting strategies of a stochastic competitive model with S-type distributed time delays and Lévy jumps

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hong Qiu ◽  
Wenmin Deng ◽  
Mingqi Xiang
Keyword(s):  
Time Delays ◽  
Sufficient Conditions ◽  
Volterra Model ◽  
Optimal Harvesting ◽  
Ergodic Method ◽  
Technical Assumption ◽  
Distributed Time Delays ◽  
Competitive Model ◽  
The Stability ◽  
Lévy Jumps

AbstractThe aim of this paper is to investigate the optimal harvesting strategies of a stochastic competitive Lotka–Volterra model with S-type distributed time delays and Lévy jumps by using ergodic method. Firstly, the sufficient conditions for extinction and stable in the time average of each species are established under some suitable assumptions. Secondly, under a technical assumption, the stability in distribution of this model is proved. Then the sufficient and necessary criteria for the existence of optimal harvesting policy are established under the condition that all species are persistent. Moreover, the explicit expression of the optimal harvesting effort and the maximum of sustainable yield are given.

Turing Instability and Hopf Bifurcation in Cellular Neural Networks

2021 ◽  
Vol 31 (08) ◽  
pp. 2150143
Author(s):  
Zunxian Li ◽  
Chengyi Xia
Keyword(s):  
Neural Networks ◽  
Hopf Bifurcation ◽  
Turing Instability ◽  
Cellular Neural Networks ◽  
Bifurcation Theorem ◽  
Decoupling Method ◽  
Dynamical Behaviors ◽  
The Stability ◽  
Approximate Expressions ◽  
Zero Equilibrium

In this paper, we explore the dynamical behaviors of the 1D two-grid coupled cellular neural networks. Assuming the boundary conditions of zero-flux type, the stability of the zero equilibrium is discussed by analyzing the relevant eigenvalue problem with the aid of the decoupling method, and the conditions for the occurrence of Turing instability and Hopf bifurcation at the zero equilibrium are derived. Furthermore, the approximate expressions of the bifurcating periodic solutions are also obtained by using the Hopf bifurcation theorem. Finally, numerical simulations are provided to demonstrate the theoretical results.

scholarly journals The Time Delays’ Effects on the Qualitative Behavior of an Economic Growth Model

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Carlo Bianca ◽  
Massimiliano Ferrara ◽  
Luca Guerrini
Keyword(s):  
Economic Growth ◽  
Growth Model ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Qualitative Behavior ◽  
Solow Model ◽  
Normal Form Theory ◽  
Economic Growth Model ◽  
Form Theory ◽  
The Stability

A further generalization of an economic growth model is the main topic of this paper. The paper specifically analyzes the effects on the asymptotic dynamics of the Solow model when two time delays are inserted: the time employed in order that the capital is used for production and the necessary time so that the capital is depreciated. The existence of a unique nontrivial positive steady state of the generalized model is proved and sufficient conditions for the asymptotic stability are established. Moreover, the existence of a Hopf bifurcation is proved and, by using the normal form theory and center manifold argument, the explicit formulas which determine the stability, direction, and period of bifurcating periodic solutions are obtained. Finally, numerical simulations are performed for supporting the analytical results.

Sensor Network Self-Organization Using Random Graphs

2009 ◽  
Vol 5 (3) ◽  
pp. 201-208 ◽  
Author(s):  
Richard R. Brooks
Keyword(s):  
Sensor Networks ◽  
Sensor Network ◽  
Random Graphs ◽  
Random Network ◽  
System Security ◽  
Peer To Peer ◽  
Critical Values ◽  
Peer Networks ◽  
Self Organization ◽  
Peer To Peer Networks

Sensor networks are deployed in, and react with, chaotic environments. Self-organizing peer-to-peer networks have admirable survivability characteristics. This chapter discusses random network formalisms for designing, modeling, and analyzing survivable sensor networks. Techniques are given for determining critical values. Applications in system security and surveillance networks are given.

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