scholarly journals An Impulse Dynamic Model for Computer Worms

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Chunming Zhang ◽  
Yun Zhao ◽  
Yingjiang Wu
Keyword(s):  
Periodic Solution ◽  
Numerical Simulations ◽  
Dynamic Model ◽  
Control Strategy ◽  
Impulsive Control ◽  
Vaccination Rate ◽  
Computer Worms ◽  
Spread Model ◽  
Impulsive Control Strategy ◽  
Globally Attractive

A worm spread model concerning impulsive control strategy is proposed and analyzed. We prove that there exists a globally attractive virus-free periodic solution when the vaccination rate is larger thanθ1. Moreover, we show that the system is uniformly persistent if the vaccination rate is less thanθ1. Some numerical simulations are also given to illustrate our main results.

scholarly journals An Impulse Model for Computer Viruses

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Chunming Zhang ◽  
Yun Zhao ◽  
Yingjiang Wu
Keyword(s):  
Periodic Solution ◽  
Control Strategy ◽  
Impulsive Control ◽  
Vaccination Rate ◽  
Computer Virus ◽  
Virus Spread ◽  
Computer Viruses ◽  
Spread Model ◽  
Impulsive Control Strategy ◽  
Globally Attractive

Computer virus spread model concerning impulsive control strategy is proposed and analyzed. We prove that there exists a globally attractive infection-free periodic solution when the vaccination rate is larger thanθ0. Moreover, we show that the system is uniformly persistent if the vaccination rate is less thanθ1. Some numerical simulations are finally given to illustrate the main results.

DYNAMIC COMPLEXITIES IN A LOTKA–VOLTERRA PREDATOR–PREY MODEL CONCERNING IMPULSIVE CONTROL STRATEGY

2005 ◽  
Vol 15 (02) ◽  
pp. 517-531 ◽  
Author(s):  
BING LIU ◽  
YUJUAN ZHANG ◽  
LANSUN CHEN
Keyword(s):  
Periodic Solution ◽  
Control Strategy ◽  
Impulsive Control ◽  
Period Doubling ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Pest Eradication ◽  
Impulsive Control Strategy

Based on the classical Lotka–Volterra predator–prey system, an impulsive differential equation to model the process of periodically releasing natural enemies and spraying pesticides at different fixed times for pest control is proposed and investigated. It is proved that there exists a globally asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value. Otherwise, the system can be permanent. We observe that our impulsive control strategy is more effective than the classical one if we take chemical control efficiently. Numerical results show that the system we considered has more complex dynamics including period-doubling bifurcation, symmetry-breaking bifurcation, period-halving bifurcation, quasi-periodic oscillation, chaos and nonunique dynamics, meaning that several attractors coexist. Finally, a pest–predator stage-structured model for the pest concerning this kind of impulsive control strategy is proposed, and we also show that there exists a globally asymptotically stable pest-eradication periodic solution when the impulsive period is less than some threshold.

scholarly journals Complex Dynamical Behaviors in a Predator-Prey System with Generalized Group Defense and Impulsive Control Strategy

2013 ◽  
Vol 2013 ◽  
pp. 1-15
Author(s):  
Shunyi Li
Keyword(s):  
Periodic Solution ◽  
Control Strategy ◽  
Impulsive Control ◽  
Period Doubling ◽  
Periodic Oscillation ◽  
Critical Value ◽  
Predator Prey ◽  
Prey System ◽  
Group Defense ◽  
Impulsive Control Strategy

A predator-prey system with generalized group defense and impulsive control strategy is investigated. By using Floquet theorem and small amplitude perturbation skills, a local asymptotically stable prey-eradication periodic solution is obtained when the impulsive period is less than some critical value. Otherwise, the system is permanent if the impulsive period is larger than the critical value. By using bifurcation theory, we show the existence and stability of positive periodic solution when the pest eradication lost its stability. Numerical examples show that the system considered has more complicated dynamics, including (1) high-order quasiperiodic and periodic oscillation, (2) period-doubling and halving bifurcation, (3) nonunique dynamics (meaning that several attractors coexist), and (4) chaos and attractor crisis. Further, the importance of the impulsive period, the released amount of mature predators and the degree of group defense effect are discussed. Finally, the biological implications of the results and the impulsive control strategy are discussed.

SYNCHRONIZATION OF IMPULSIVELY COUPLED SYSTEMS

2008 ◽  
Vol 18 (05) ◽  
pp. 1539-1549 ◽  
Author(s):  
XIUPING HAN ◽  
JUN-AN LU ◽  
XIAOQUN WU
Keyword(s):  
Dynamical Systems ◽  
Control Strategy ◽  
Impulsive Control ◽  
Coupled Model ◽  
Coupled Systems ◽  
Single System ◽  
Impulsive Synchronization ◽  
The Past ◽  
Impulsive Control Strategy ◽  
Control And Synchronization

In the past years, impulsive control for a single system and impulsive synchronization between two systems have been extensively studied. However, investigation on impulsive control and synchronization of complex networks has just started. In these studies, a network is continuously coupled, and then is synchronized by using impulsive control strategy. In this paper, a new and different coupled model is proposed, where the systems are coupled only at discrete instants through impulsive connections. Several criteria for synchronizing such kind of impulsively coupled complex dynamical systems are established. Two examples are also worked through for illustrating the main results.

scholarly journals Complex Behavior in a Fish Algae Consumption Model with Impulsive Control Strategy

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Jin Yang ◽  
Min Zhao
Keyword(s):  
Control Strategy ◽  
Small Amplitude ◽  
Impulsive Control ◽  
Asymptotically Stable ◽  
Perturbation Techniques ◽  
Globally Asymptotically Stable ◽  
Impulsive Equations ◽  
Consumption Model ◽  
The Rich ◽  
Impulsive Control Strategy

This paper investigates a dynamic mathematical model of fish algae consumption with an impulsive control strategy analytically. It is proved that the system has a globally asymptotically stable algae-eradication periodic solution and is permanent by using the theory of impulsive equations and small-amplitude perturbation techniques. Numerical results for impulsive perturbations demonstrate the rich dynamic behavior of the system. Further, we have also compared biological control with chemical control. All these results may be useful in controlling eutrophication.

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