PIECEWISE CONTINUOUS SOLUTIONS OF INITIAL VALUE PROBLEMS OF SINGULAR FRACTIONAL DIFFERENTIAL EQUATIONS WITH IMPULSE EFFECTS

Results on the existence of piecewise continuous solutions for two classes of initial value problems of impulsive singular fractional differential equations are obtained.

A Kind of Predator-prey System of Holling Type II and Interaction Perturbation with Impulsive Effect

A kind of predator-prey system of Holling typeⅡand interaction perturbation with impulsive effect is presented.By using Floquet theory and small amplitude perturbations skills,the locally asymptotical stability of prey-eradication periodic solution and the permanence of the system are discussed and the corresponding threshold conditions are given respectively.Finally,the existence of positive periodic solution is investigated by the bifurcation theory.

A Stage-structured Predator-prey Model with Time Delay and Impulsive Effects

A delayed predator-prey model concerning impulsive spraying pesticides and releasing natural enemies is proposed and investigated,in which both the prey and the predator have a history that takes them through two stages:immature and mature.The global attractiveness of the pest-eradication periodic solution is discussed,and sufficient condition is obtained for the permanence of the system.Further,numerical simulations show that there is a characteristic sequence of bifurcations leading to a chaotic dynamics,which implies that the system with constant periodic impulsive perturbations admits rich and complex dynamics.

Nontrivial Homoclinic Solutions for Second-Order p-Laplacian Differential System with Impulsive Effects

The existence of homoclinic solutions for the second-order p-Laplacian differential system( ρ( t) Φp( u'( t))) '-s( t) Φp( u( t))+ λf( t,u( t)) = 0 with impulsive effects Δ( ρ( tj) Φp( u'( tj))) = Ij( u( tj)) is studied. By using three critical points theorem and variational methods, the sufficient condition is established to guarantee that this p-Laplacian differential system with impulsive effects has at least one nontrivial homoclinic solution. Besides,an example is presented to illustrate the main result in the end of this paper.

Impulsive effect on exponential synchronization of neural networks with leakage delay under sampled-data feedback control

We consider the impulsive effect on the exponential synchronization of neural networks with leakage delay under the sampled-data feedback control. We use an appropriate Lyapunov-Krasovskii functional combined with the input delay approach and some inequality techniques to derive sufficient conditions that ensure the exponential synchronization of the delayed neural network. The conditions are formulated in terms of the leakage delay, the sampling period, and the exponential convergence rate. Numerical examples are given to demonstrate the usefulness and the effectiveness of the results.

Effective Impulse for Fully Clamped Rectangular Plates Under Internal Blast Loading

Under internal blast loading,the response of a beam or plate is highly correlated with the phenomenon of saturated impulse,which governs the deflection of the structure.This paper aims to investigate the phenomenon of saturated impulse for fully clamped rectangular plates subjected to internal blast loading.Based on the rigid,perfectly plastic assumption,the relationship between saturation duration and saturation deflection is derived.Influences of the peak shock wave,the duration of shock wave and the peak quasi-static pressure loading on saturation duration and saturation deflection are discussed.It is found that there is a critical duration for the internal blast impulse to reach saturation,and beyond this duration,the deflection of plate will no longer increase as the loading increases further.The saturation deflection and saturation duration both exhibit regular variation patterns with the changes of the dimensionless peak shock wave,the duration of shock wave and the peak quasi-static pressure loading.

Experimental research on impulse coupling effect of a multi-pulse laser on an aluminum target

Impact and torsion pendulums are applied in impulse coupling experiments of high-energy laser irradiation of space debris. It is difficult to achieve a multi-pulse experiment and thus hard to analyze the multi-pulse impulse coupling effect. Here, we designed a new recoil impulse experimental measurement system of non-contact, multidegrees of freedom, and multi-pulse irradiation. The system used a low-pressure and low-temperature vacuum chamber to simulate the space environment, the pinning effect of magnetic levitation to achieve aluminum target suspension, and high-speed cameras to record the displacement over time to calculate the impulse of the target.Then the impulse coupling experiment of multi-pulse laser irradiation on the aluminum target was performed.The result shows that the multi-pulse impulse coupling effect is not the linear accumulation of coupling results by every single-pulse and multi-pulse coefficient that decreases with the increase of the number of pulses, and eventually stabilizes as the decrease gets smaller.

A Stage-Structured Predator-Prey System with Impulsive Effect and Holling Type-Ⅱ Functional Response

A stage-structured predator-prey system with impulsive effect and Holling type-II functional response is investigated. By the Floquet theory and small amplitude perturbation skills, it is proved that there exists a global stable pest-eradication periodic solution when the impulsive period is less than some critical values. Farther, the conditions for the permanence of system are established. Numerical simulations are carried out to illustrate the impulsive effect on the dynamics of the system.

Existence of Positive Periodic Solution of Periodic Time-Dependent Predator-Prey System with Impulsive Effects

The general system of differential equations describing predator-prey dynamics with impulsive effects is modified by the assumption that the coefficients are periodic functions of time. By use of standard techniques of bifurcation theory, it is known that this system has a positive periodic solution provided the time average of the predator’s net uninhibited death rate is in a suitable range. The bifurcation is from the periodic solution of the time-dependent logistic equation for the prey (which results in the absence of predator).

Synchronization of switched Boolean networks with impulsive effects

This paper studies the state/output synchronization of switched Boolean networks （SBNs） with impulsive effects via the algebraic state space representation （ASSR） approach. First, an algebraic form is established for SBNs with impulsive effects via ASSR. Second, based on the algebraic form, some necessary and sufficient conditions are presented for the state/output synchronization of SBNs with impulsive effects under arbitrary switching signals. Third, two special kinds of switching signals, that is, free switching signal and feedback switching signal, are considered for the state synchroniza-tion of SBNs with impulsive effects. Finally, two illustrative examples are worked out to show the effectiveness of the obtained results.

A DELAYED RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH STAGE-STRUCTURED AND IMPULSIVE EFFECT

In this paper, a delayed ratio-dependent Holling-III predator-prey system with stagestructured and impulsive stocking on prey and continuous harvesting on predator is considered. The authors obtain sufficient conditions of the global attractivity of predator-extinction periodic solution and the permanence of the system. These＇ results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system. The authors also prove that all solutions of the system are uniformly ultimately bounded. The results show that the biological resource management is effective and reliable. Key words Globally attractivity, impulsive effect, permanence, ratio-dependent, stage-structured.

Dynamics of a stage-structured single population system with winter hibernation and impulsive effect in polluted environment

In this work, we construct a stage-structured single population system with winter hiber- nation and impulsive effect in polluted environment. All solutions of the investigated system are proved to be uniformly ultimately bounded. The conditions of the population- extinction solution of the investigated system are obtained. The permanent condition of the investigated system is also obtained. Finally, numerical analysis is inserted to illustrate the results. Our results indicate that the environmental pollution will reduce biological diversity of the natural world. Our results also provide reliable tactic basis for the practical biological resource management.

THE PERIODIC VOLTERRA MODEL WITH MUTUAL INTERFERENCE AND IMPULSIVE EFFECT

In this paper, a periodic Volterra model with mutual interference and impulsive effect is proposed and analyzed. By applying the Floquet theory of impulsive differential equa- tion, some conditions are obtained for the linear stability of semi-trivial periodic solution. Some sufficient conditions are also given for the permanence of the system. Further, stan- dard bifurcation theory is used to show the existence of coexistence state which arises near the semi-trivial periodic solution. Finally, theoretical results are confirmed by some special cases of the system.

THE PERIODIC HOLLING Ⅱ PREDATOR-PREY MODEL WITH IMPULSIVE EFFECT

In this paper, a periodic Holling Ⅱ predator-prey model with impulsive effect is investigated. By applying the Floquet theory of linear periodic impulsive equation,some sufficient conditions are obtained for the linear stability and instability of trivial and semi-trivial periodic solutions. Moreover, we use standard bifurcation theory to show the existence of coexistence states which arise near the semi-trivial periodic solution. As an application, we also examine some special case of the system to confirm our main results.

Set Stability of Probabilistic Time-Delay Boolean Networks with Impulsive Effect

This paper investigates the set stability of probabilistic time-delay Boolean networks(PTDBN)with impulsive effect.Firstly,using the algebraic state space representation,an equivalent stochastic system is established for PTDBN with impulsive effect.Then,based on the probabilistic state transition matrix,a necessary and sufficient condition is presented for the set stability of PTDBN with impulsive effect.Finally,the obtained new result is applied to the networked evolutionary game with memories.

Dynamics for a hybrid non-autonomous prey-predator system with generalist predator and impulsive conditions on time scales

In this paper,we investigate the dynamical behavior for a hybrid non-autonomous predator-prey system with Holling Type II functional response,impulsive effects and generalist predator on time scales,where our proposed model commutes between a continuous-time dynamical system and discrete-time dynamical system.By using com--parison theorems,we first study the permanence results of the proposed model.Also,we established the uniformly asymptotic stability for the almost periodic solution of the proposed model.Finally,in the last section,we provide some examples with numerical simulation.

The Dynamics of a Predator-prey Model with Ivlev's Functional Response Concerning Integrated Pest Management

A mathematical model of a predator-prey model with Ivlev’s functional response concerning integrated pest management (IPM) is proposed and analyzed. We show that there exists a stable pest-eradication periodic solution when the impulsive period is less than some critical values. Further more, the conditions for the permanence of the system are given. By using bifurcation theory, we show the existence and stability of a positive periodic solution. These results are quite different from those of the corresponding system without impulses. Numerical simulation shows that the system we consider has more complex dynamical behaviors. Finally, it is proved that IPM stragey is more effective than the classical one.

A STAGE-STRUCTURED SI ECO-EPIDEMIOLOGICAL MODEL WITH TIME DELAY AND IMPULSIVE CONTROLLING

This paper formulates a robust stage-structured SI eco-epidemiological model with periodic constant pulse releasing of infectious pests with pathogens. The authors show that the conditions for global attractivity of the ＇pest-eradication＇ periodic solution and permanence of the system depend on time delay, hence, the authors call it ＂profitless＂. Further, the authors present a pest management strategy in which the pest population is kept under the economic threshold level （ETL） when the pest population is uniformly persistent. By numerical analysis, the authors also show that constant maturation time delay for the susceptible pests and pulse releasing of the infectious pests can bring obvious effects on the dynamics of system.

The Dynamics of a Prey-dependent Consumption Model Concerning Integrated Pest Management

A mathematical model for the dynamics of a prey-dependent consumption model concerning integrated pest management is proposed and analyzed. We show that there exists a globally stable pesteradication periodic solution when the impulsive period is less than some critical values. Furthermore, the conditions for the permanence of the system are given. By using bifurcation theory, we show the existence of a nontrival periodic solution if the pest-eradication periodic solution loses its stability. When the unique positive periodic solution loses its stability, numerical simulation shows there is a characteristic sequence of bifurcations, leading to a chaotic dynamics, which implies that dynamical behaviors of prey-dependent consumption concerning integrated pest management are very complex, including period-doubling cascades, chaotic bands with periodic windows, crises, symmetry-breaking bifurcations and supertransients.

New results on impulsive type inertial bidirectional associative memory neural networks

This paper is concerned with inertial bidirectional associative memory neural networks with mixed delays and impulsive effects.New and practical conditions are given to study the existence,uniqueness,and global exponential stability of anti-periodic solutions for the suggested system.We use differential inequality techniques to prove our main results.Finally,we give an illustrative example to demonstrate the effectiveness of our new results.