Synchronization of Epidemic Systems with Neumann Boundary Value under Delayed Impulse

Abstract

This paper reports the construction of synchronization criteria for the delayed impulsive epidemic models with reaction–diffusion under the Neumann boundary value. Different from the previous literature, the reaction–diffusion epidemic model with a delayed impulse brings mathematical difficulties to this paper. In fact, due to the existence of second-order partial derivatives in the reaction–diffusion model with a delayed impulse, the methods of first-order ordinary differential equations from the previous literature cannot be effectively applied in this paper. However, with the help of the variational method and an appropriate boundedness assumption, a new synchronization criterion is derived, and its effectiveness is illustrated by numerical examples.

Impulsive Control and Synchronization for Fractional-Order Hyper-Chaotic Financial System

“…(I + L) T P(I + L) < P, (10) then the system (3) achieves global Mittag-Leffler synchronization with System (1), where I is the identity matrix, and…”

“…and numerical examples show that as long as the impulsive macroeconomic management measures are appropriate, the backward economic system can gradually synchronize with the advanced economic system. Finally, the impulsive control involving time delay and the impulsive control under trigger event mechanism still need to be studied for the mathematical model of macroeconomics( [10][11][12]).…”

“…LMI-toolbox to solve LMI conditions(9) and(10) results in the following feasibility data: = 0.5013 According to Theorem 1, System (3) is global Mittag-Leffler synchronization with System (1).…”

The existence and averaging principle for stochastic fractional differential equations with impulses

“…Therefore, impulsive fractional stochastic differential equations are generally used in many scientific branches, such as biology, economics, finance, telecommunications, electronics and medicine 19,20 . In recent years, some researchers have studied the delayed impulsive epidemic model with reaction‐diffusion 21 . Similarly, differential equations with impulses have also attracted the attention of many scholars studying stability 22–25 .…”

Impulsive Control and Synchronization for Fractional-Order Hyper-Chaotic Financial System

“…-toolbox to solve LMI conditions(9) and(10) results in the following feasibility data: ε 1 = 0.4996 According to Theorem 1, the system (5) is global Mittag-Leffler synchronization with the system (2) (see Fig.8-11).…”