scholarly journals Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems

2012 ◽  
Vol 85 (5) ◽  
Author(s):  
Thomas E. Woolley ◽  
Ruth E. Baker ◽  
Eamonn A. Gaffney ◽  
Philip K. Maini ◽  
Sungrim Seirin-Lee
Keyword(s):  
Reaction Diffusion ◽  
Delayed Reaction ◽  
Intrinsic Stochasticity

scholarly journals Bifurcation Analysis in a Diffusive Mussel-Algae Model with Delay

2019 ◽  
Vol 29 (11) ◽  
pp. 1950144 ◽  
Author(s):  
Zuolin Shen ◽  
Junjie Wei
Keyword(s):  
Hopf Bifurcation ◽  
Functional Differential Equations ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Delayed Reaction ◽  
Center Manifold Reduction ◽  
Existence Of Positive Solutions ◽  
Boundary Equilibrium ◽  
Functional Differential ◽  
The Stability

In this paper, we consider the dynamics of a delayed reaction–diffusion mussel-algae system subject to Neumann boundary conditions. When the delay is zero, we show the existence of positive solutions and the global stability of the boundary equilibrium. When the delay is not zero, we obtain the stability of the positive constant steady state and the existence of Hopf bifurcation by analyzing the distribution of characteristic values. By using the theory of normal form and center manifold reduction for partial functional differential equations, we derive an algorithm that determines the direction of Hopf bifurcation and the stability of bifurcating periodic solutions. Finally, some numerical simulations are carried out to support our theoretical results.

scholarly journals Modeling Cell-to-Cell Spread of HIV-1 with Nonlocal Infections

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Xiaoting Fan ◽  
Yi Song ◽  
Wencai Zhao
Keyword(s):  
Reproduction Number ◽  
Reaction Diffusion ◽  
Threshold Dynamics ◽  
Delayed Reaction ◽  
Heterogeneous Model ◽  
Host Environment ◽  
Reaction Diffusion Model ◽  
Globally Attractive ◽  
Cell Spread ◽  
Hiv 1

This paper is devoted to develop a nonlocal and time-delayed reaction-diffusion model for HIV infection within host cell-to-cell viral transmissions. In a bounded spatial domain, we study threshold dynamics in terms of basic reproduction number R0 for the heterogeneous model. Our results show that if R0<1, the infection-free steady state is globally attractive, implying infection becomes extinct, while if R0>1, virus will persist in the host environment.

scholarly journals Regularity of a Stochastic Fractional Delayed Reaction-Diffusion Equation Driven by Lévy Noise

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Tianlong Shen ◽  
Jianhua Huang ◽  
Jin Li
Keyword(s):  
Fixed Point ◽  
Diffusion Equation ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Banach Fixed Point Theorem ◽  
Fractional Operator ◽  
Initial Value ◽  
Delayed Reaction

The current paper is devoted to the regularity of the mild solution for a stochastic fractional delayed reaction-diffusion equation driven by Lévy space-time white noise. By the Banach fixed point theorem, the existence and uniqueness of the mild solution are proved in the proper working function space which is affected by the delays. Furthermore, the time regularity and space regularity of the mild solution are established respectively. The main results show that both time regularity and space regularity of the mild solution depend on the regularity of initial value and the order of fractional operator. In particular, the time regularity is affected by the regularity of initial value with delays.

scholarly journals Exponential Stability and Periodicity of Fuzzy Delayed Reaction-Diffusion Cellular Neural Networks with Impulsive Effect

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Guowei Yang ◽  
Yonggui Kao ◽  
Changhong Wang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Cellular Neural Networks ◽  
Impulsive Effect ◽  
Time Varying ◽  
Delayed Reaction

This paper considers dynamical behaviors of a class of fuzzy impulsive reaction-diffusion delayed cellular neural networks (FIRDDCNNs) with time-varying periodic self-inhibitions, interconnection weights, and inputs. By using delay differential inequality,M-matrix theory, and analytic methods, some new sufficient conditions ensuring global exponential stability of the periodic FIRDDCNN model with Neumann boundary conditions are established, and the exponential convergence rate index is estimated. The differentiability of the time-varying delays is not needed. An example is presented to demonstrate the efficiency and effectiveness of the obtained results.

scholarly journals Adaptive stochastic synchronization of delayed reaction–diffusion neural networks

2020 ◽  
Vol 53 (3-4) ◽  
pp. 378-389 ◽  
Author(s):  
Weiyuan Zhang ◽  
Junmin Li ◽  
Jinghan Sun ◽  
Minglai Chen
Keyword(s):  
Neural Networks ◽  
Feedback Control ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Linear Matrix ◽  
Output Coupling ◽  
Delayed Reaction ◽  
Adaptive Feedback ◽  
Adaptive Feedback Control ◽  
Stochastic Synchronization

In this paper, we deal with the adaptive stochastic synchronization for a class of delayed reaction–diffusion neural networks. By combing Lyapunov–Krasovskii functional, drive-response concept, the adaptive feedback control scheme, and linear matrix inequality method, we derive some sufficient conditions in terms of linear matrix inequalities ensuring the stochastic synchronization of the addressed neural networks. The output coupling with delay feedback and the update laws of parameters for adaptive feedback control are proposed, which will be of significance in the real application. The novel Lyapunov–Krasovskii functional to be constructed is more general. The derived results depend on the measure of the space, diffusion effects, and the upper bound of derivative of time-delay. Finally, an illustrated example is presented to show the effectiveness and feasibility of the proposed scheme.

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