MULTIPLE POSITIVE PERIODIC SOLUTIONS IN A IMPULSIVE PREDATOR-PREY SYSTEM WITH TYPEⅣFUNCTIONAL RESPONSES

The main purpose of this paper is to explore the existence of positive periodic solutions to impulsive predator-prey systems with type IV functional responses. Sufficient criteria are obtained for the existence of strictly positive periodic solutions. The approach is based on a continuation theorem in the coincidence degree theory as well as some prior estimates. This is also the first time that multiple positive periodic solutions are obtained using coincidence degree theory in impulsive ecological systems.

Analysis and Design of Time-Delay Impulsive Systems Subject to Actuator Saturation

This paper investigates the exponential stability and performance analysis of nonlinear time-delay impulsive systems subject to actuator saturation. When continuous dynamics is unstable, under some conditions, it is shown that the system can be stabilized by a class of saturated delayed-impulses regardless of the length of input delays. Conversely, when the system is originally stable, it is shown that under some conditions, the system is robust with respect to sufficient small delayed-impulses. Moreover, the design problem of the controller with the goal of obtaining a maximized estimate of the domain of attraction is formulated via a convex optimization problem. Three examples are provided to demonstrate the validity of the main results.

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.

PCA-LSTM:An Impulsive Ground-Shaking Identification Method Based on Combined Deep Learning

Near-fault impulsive ground-shaking is highly destructive to engineering structures,so its accurate identification ground-shaking is a top priority in the engineering field.However,due to the lack of a comprehensive consideration of the ground-shaking characteristics in traditional methods,the generalization and accuracy of the identification process are low.To address these problems,an impulsive ground-shaking identification method combined with deep learning named PCA-LSTM is proposed.Firstly,ground-shaking characteristics were analyzed and groundshaking the data was annotated using Baker’smethod.Secondly,the Principal Component Analysis(PCA)method was used to extract the most relevant features related to impulsive ground-shaking.Thirdly,a Long Short-Term Memory network(LSTM)was constructed,and the extracted features were used as the input for training.Finally,the identification results for the Artificial Neural Network(ANN),Convolutional Neural Network(CNN),LSTM,and PCA-LSTMmodels were compared and analyzed.The experimental results showed that the proposed method improved the accuracy of pulsed ground-shaking identification by>8.358%and identification speed by>26.168%,compared to other benchmark models ground-shaking.

Lyapunov Conditions for Finite-Time Input-to-State Stability of Impulsive Switched Systems

Dear Editor,This letter studies finite-time input-to-state stability(FTISS)for impulsive switched systems.A set of Lyapunov-based conditions are established for guaranteeing FTISS property.When constituent modes governing continuous dynamics are FTISS and discrete dynamics involving impulses are destabilizing,the FTISS can be retained if impulsive-switching signals satisfy an average dwell-time(ADT)condition.

Delayed stage-structured predator-prey model with impulsive perturbations on predator and chemical control on prey

We consider a delayed stage-structured pest management predator-prey system with impulsive transmitting on predator and chemical control on prey. Sufficient conditions of the global attractiveness of the pest-extinction boundary periodic solution and permanence of the system are obtained. We also prove that all solutions of the system are uniformly ultimately bounded. Our results provide reliable tactical basis for practical pest management.

Permanence and global attractivity of stage-structured predator-prey model with continuous harvesting on predator and impulsive stocking on prey

We investigate a stage-structured delayed predator-prey model with impulsive stocking on prey and continuous harvesting on predator. According to the fact of biological resource management, we improve the assumption of a predator-prey model with stage structure for predator population that each individual predator has the same ability to capture prey. It is assumed that the immature and mature individuals of the predator population are divided by a fixed age, and immature predator population does not have the ability to attach prey. Sufficient conditions are obtained, which guarantee the global attractivity of predator-extinction periodic solution and the permanence of the system. Our results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system, and provide tactical basis for the biological resource management. Numerical analysis is presented to illuminate the dynamics of the system.

Modeling Near-Field Impulsive Waves Generated by Deformable Landslide Using the HBP Model Based on the SPH Method

Landslide-generated impulsive waves(LGWs)in reservoir areas can seriously threaten waterway safety as well as hu-man life and properties around the two side slopes.The risk reduction and mitigation of such a hazard require the accurate prediction of near-field wave characteristics,such as wave amplitude and run-up.However,near-field LGW involves complicated fluid-solid interactions.Furthermore,the wave characteristics are closely related to various aspects,including the geometry and physical features of the slide,river,and body of water.However,the empirical or analytical methods used for rough estimation cannot derive accurate results,especially for deformable landslides,due to their significant geometry changes during the sliding process.In this study,the near-field waves generated by deformable landslides were simulated by smoothed particle hydrodynamics(SPH)based on multi-phase flow.The deformable landslides were generalized as a kind of viscous flow by adopting the Herschel-Bulkley-Papanastasiou(HBP)-based nonNewtonian rheology model.The HBP model is capable of producing deformable landslide dynamics even though the high-speed sliding process is involved.In this study,an idealized experiment case originating from Lituya LGW and a practical case of Gongjiafang LGW were reproduced for verification and demonstration.The simulation results of both cases show satisfactory consistency with the experiment/investigation data in terms of landslide movement and near-field impulsive wave characteristics,thus indicating the applicability and accuracy of the proposed method.Finally,the effects of the HBP model’s rheological parameters on the landslide dynamics and near-field wave characteristics are discussed,providing a parameter calibration method along with sug-gestions for further applications.

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.

Localization for mixed near-field and far-field sources under impulsive noise

In order to solve the problem that the performance of traditional localization methods for mixed near-field sources(NFSs)and far-field sources(FFSs)degrades under impulsive noise,a robust and novel localization method is proposed.After eliminating the impacts of impulsive noise by the weighted out-lier filter,the direction of arrivals(DOAs)of FFSs can be estimated by multiple signal classification(MUSIC)spectral peaks search.Based on the DOAs information of FFSs,the separation of mixed sources can be performed.Finally,the estimation of localizing parameters of NFSs can avoid two-dimension spectral peaks search by decomposing steering vectors.The Cramer-Rao bounds(CRB)for the unbiased estimations of DOA and range under impulsive noise have been drawn.Simulation experiments verify that the proposed method has advantages in probability of successful estimation(PSE)and root mean square error(RMSE)compared with existing localization methods.It can be concluded that the proposed method is effective and reliable in the environment with low generalized signal to noise ratio(GSNR),few snapshots,and strong impulse.

Numerical Study of the Vibrations of Beams with Variable Stiffness under Impulsive or Harmonic Loading

The behavior of beams with variable stiffness subjected to the action of variable loadings (impulse or harmonic) is analyzed in this paper using the successive approximation method. This successive approximation method is a technique for numerical integration of partial differential equations involving both the space and time, with well-known initial conditions on time and boundary conditions on the space. This technique, although having been applied to beams with constant stiffness, is new for the case of beams with variable stiffness, and it aims to use a quadratic parabola (in time) to approximate the solutions of the differential equations of dynamics. The spatial part is studied using the successive approximation method of the partial differential equations obtained, in order to transform them into a system of time-dependent ordinary differential equations. Thus, the integration algorithm using this technique is established and applied to examples of beams with variable stiffness, under variable loading, and with the different cases of supports chosen in the literature. We have thus calculated the cases of beams with constant or variable rigidity with articulated or embedded supports, subjected to the action of an instantaneous impulse and harmonic loads distributed over its entire length. In order to justify the robustness of the successive approximation method considered in this work, an example of an articulated beam with constant stiffness subjected to a distributed harmonic load was calculated analytically, and the results obtained compared to those found numerically for various steps (spatial h and temporal τ ¯ ) of calculus, and the difference between the values obtained by the two methods was small. For example for ( h=1/8 , τ ¯ =1/ 64 ), the difference between these values is 17%.

Force and impulse multi-sensor based on flexible gate dielectric field effect transistor

Nowadays,force sensors play an important role in industrial production,electronic information,medical health,and many other fields.Two-dimensional material-based filed effect transistor(2D-FET)sensors are competitive with nano-level size,lower power consumption,and accurate response.However,few of them has the capability of impulse detection which is a path function,expressing the cumulative effect of the force on the particle over a period of time.Herein we fabricated the flexible polymethyl methacrylate(PMMA)gate dielectric MoS_(2)-FET for force and impulse sensor application.We systematically investigated the responses of the sensor to constant force and varying forces,and achieved the conversion factors of the drain current signals(I_(ds))to the detected impulse(I).The applied force was detected and recorded by I_(ds)with a low power consumption of~30 nW.The sensitivity of the device can reach~8000%and the 4×1 sensor array is able to detect and locate the normal force applied on it.Moreover,there was almost no performance loss for the device as left in the air for two months.

Existence of Periodic Solution for a Non-Autonomous Stage-Structured Predator-Prey System with Impulsive Effects

In this paper, we studied a non-autonomous predator-prey system where the prey dispersal in a two-patch environment. With the help of a continuation theorem based on coincidence degree theory, we establish sufficient conditions for the existence of positive periodic solutions. Finally, we give numerical analysis to show the effectiveness of our theoretical results.

Dynamical Analysis of a Stochastic Predator-Prey System with Lévy Noise and Impulsive Toxicant Input

This paper established a modified Leslie-Gower and Holling-type IV stochastic predator-prey model with Lévy noise and impulsive toxicant input. We study the stability in distribution of solutions by inequality techniques and ergodic method. By comparison method and Itô’s formula, we obtain the sufficient conditions for the survival of each species. Some numerical simulations are introduced to show the theoretical results.

Impulsive Predator-Prey Dynamic Systems with Beddington-DeAngelis Type Functional Response on the Unification of Discrete and Continuous Systems

In this study, the impulsive predator-prey dynamic systems on time scales calculus are studied. When the system has periodic solution is investigated, and three different conditions have been found, which are necessary for the periodic solution of the predator-prey dynamic systems with Beddington-DeAngelis type functional response. For this study the main tools are time scales calculus and coincidence degree theory. Also the findings are beneficial for continuous case, discrete case and the unification of both these cases. Additionally, unification of continuous and discrete case is a good example for the modeling of the life cycle of insects.

PERMANENCE OF AN IMPULSIVE PREDATOR-PREY SYSTEM WITH MUTUAL INTERFERENCE AND CROWLEY-MARTIN RESPONSE FUNCTION

In this paper, we investigated an impulsive predator-prey model with mu- tual interference and Crowley-Martin response function. By the comparison theorem and the analysis technique of [12,14], sufficient conditions for the per-manence of the impulsive model are obtained, which generalizes one of main results of [4].

Impulsive Logistic Model for Gray Leaf Spots Caused by Cercospora zeae-maydi

[ Objectlve] Impulsive Logistic Model was used to simulate epidemic process of Gray Leaf Spots caused by C. zeae-maydi. [ Method] The pathogen was inoculated in different maize varieties, and the incidence were observed and recorded. Impulsive Logistic Model was used to simulate the development process of the disease, which was compared with actual incidence. [ Result] Artificial inoculation tests showed that impulsive Logistic Model could reflect time dynamic of C. zeae-maydi. Through derivation, exponential growth phase was from maize seedling emergence to eady July in each year, logistic phase was from early July to late August, terminal phase was from eady September to the end of maize growth stage. [ Conclusion] The derivation result from model was consistent with the development biological laws of C. zeae-maydi.

The Global Solutions of Impulsive Retarded Functional Differential Equations

In this paper, we present some results on the existence of the golbal solutions of nonlinear impulsive retarded functional differential equations.

Interval analysis method and convex models for impulsive response of structures with uncertain-but-bounded external loads

Two non-probabilistic, set-theoretical methods for determining the maximum and minimum impulsive responses of structures to uncertain-but-bounded impulses are presented. They are, respectively, based on the theories of interval mathematics and convex models. The uncertain-but-bounded impulses are assumed to be a convex set, hyper-rectangle or ellipsoid. For the two non-probabilistic methods, less prior information is required about the uncertain nature of impulses than the probabilistic model. Comparisons between the interval analysis method and the convex model, which are developed as an anti-optimization problem of finding the least favorable impulsive response and the most favorable impulsive response, are made through mathematical analyses and numerical calculations. The results of this study indicate that under the condition of the interval vector being determined from an ellipsoid containing the uncertain impulses, the width of the impulsive responses predicted by the interval analysis method is larger than that by the convex model; under the condition of the ellipsoid being determined from an interval vector containing the uncertain impulses, the width of the interval impulsive responses obtained by the interval analysis method is smaller than that by the convex model.

ON BOUNDEDNESS OF SOLUTIONS OFIMPULSIVE INTEGRO-DIFFERENTIAL SYSTEMSWITH FIXED MOMENTS OF IMPULSE EFFECTS

Several boundedness criteria for the impulsive integro-differential systems with fixed moments of impulse effects are established, employing the method of Lyapunov functions and Razumikhin technique.