Search

Your search keyword '"*DELAY differential equations"' showing total 4 results
Start Over Descriptor "*DELAY differential equations" Topic stability Publication Year Range This year Publisher elsevier b.v.
4 results on '"*DELAY differential equations"'

1. Stability of impulsive stochastic functional differential equations with delays.

Author

Guo, Jingxian, Xiao, Shuihong, and Li, Jianli

Subjects
*DELAY differential equations, *STOCHASTIC differential equations, *FUNCTIONAL differential equations, *IMPULSIVE differential equations, *STABILITY criterion, *LYAPUNOV functions
Abstract

In this paper, we consider the global asymptotical stability of stochastic functional differential equations with impulsive effects. First, by constructing the Lyapunov function, some stability criteria of impulsive stochastic functional differential equations are established. Second, we propose an application to investigate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

Published
2024
Full Text
View/download PDF

2. Boundedness and stability of nonlinear hybrid neutral stochastic delay differential equation with Lévy jumps under different structures.

Author

Song, Ruili, Zhao, Jiayu, and Zhu, Quanxin

Subjects
*STOCHASTIC differential equations, *HYBRID systems, *EXPONENTIAL stability, *DELAY differential equations, *LYAPUNOV functions, *MATRICES (Mathematics)
Abstract

This paper investigates the boundedness and stability of a class of nonlinear hybrid neutral stochastic differential delay systems with Lévy jumps and different structures. The coefficients in this system satisfy the local Lipschitz condition and a suitable Khasminskii-type condition, and the state space of the system is separated into two subsets, the existence uniqueness, asymptotic boundedness, and exponential stability of the system are obtained by designing a new Lyapunov function and applying the M-matrix technique as well as dealing with the non-differentiable delay function. Different with the existing work, we not only consider the neutral term, but also the case of the delay function being bounded and non-differentiable. At last, numerical examples are performed to manifest the obtained results. [ABSTRACT FROM AUTHOR]

Published
2024
Full Text
View/download PDF

3. Delay differential equation modeling of social contagion with higher-order interactions.

Author

Lv, Xijian, Fan, Dongmei, Yang, Junxian, Li, Qiang, and Zhou, Li

Subjects
*CONTAGION (Social psychology), *SOCIAL interaction, *SOCIAL values, *SYSTEM dynamics, *DELAY differential equations
Abstract

In this paper, we propose a social contagion model with group interactions on heterogeneous network, in which the group interactions are represented by incorporating higher-order terms. The dynamics of the proposed model are analyzed, revealing the effect of group interactions on the system dynamics. We derive a global asymptotically stability condition of the zero equilibrium point. If the parameters enhancement factor and transform probability meet the condition, the social contagion will eventually disappear. The bifurcation behavior arising from group interactions is investigated, when the enhancement factor exceeds a threshold, the system undergoes a backward bifurcation. This implies that R 0 < 1 does not guarantee the disappearance of social contagion, we also need to control the initial values of social contagion at a lower level. The optimal control strategies for the model are provided. Moreover, the numerical simulations validate the accuracy of the theoretical analysis. It is worth noting that the group interactions lead to the emergence of a bistable phenomenon, in which the social contagion will either fade away or persist eventually, depending on the initial values. • The simplicial SIS social contagion model with delay is proposed on heterogeneous networks. • The dynamics of the model are analyzed, revealing the effect of group interactions on the system dynamics. • An optimal control strategy is proposed for the model, incorporating group interactions. [ABSTRACT FROM AUTHOR]

Published
2024
Full Text
View/download PDF

4. Stability of coupled Wilson–Cowan systems with distributed delays.

Author

Kaslik, Eva, Kökövics, Emanuel-Attila, and Rădulescu, Anca

Subjects
*GAMMA distributions, *LARGE-scale brain networks, *BASAL ganglia, *DYNAMICAL systems, *DELAY differential equations
Abstract

Building upon our previous work on the Wilson-Cowan equations with distributed delays (Kaslik et al., 2022), we study the dynamic behavior in a system of two coupled Wilson-Cowan pairs. We focus in particular on understanding the mechanisms that govern the transitions in and out of oscillatory regimes associated with pathological behavior. We investigate these mechanisms under multiple coupling scenarios, and we compare the effects of using discrete delays versus a weak Gamma delay distribution. We found that, in order to trigger and stop oscillations, each kernel emphasizes different critical combinations of coupling weights and time delay, with the weak Gamma kernel restricting oscillations to a tighter locus of coupling strengths, and to a limited range of time delays. We finally illustrate the general analytical results with simulations for two particular applications: generation of beta-rhythms in the basal ganglia, and alpha oscillations in the prefrontal-limbic system. • We study long-term dynamics in coupled Wilson–Cowan systems with distributed delays. • Our analysis focuses on understanding the system's transitions in and out of stable oscillations. • We study how these transitions change under different connectivity schemes and strengths. • We explore the effects of different delay distributions and average delay values. • The analysis is illustrated with simulations in two different functional brain networks. [ABSTRACT FROM AUTHOR]

Published
2024
Full Text
View/download PDF

Catalog

Books, media, physical & digital resources
See catalog results