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This paper is devoted to a nonlocal dispersal logistic model with seasonal succession and free boundaries, where the free boundaries represent the expanding front and the seasonal succession accounts for the effect of two different seasons. Technically, this free boundary problem is much more difficult than the case without seasonal succession since the coefficients are all time periodic and piecewise continuous. We prove the existence and uniqueness of global solution, and then examine the long-time dynamical behaviour and the criteria that completely determine when spreading and vanishing can happen, revealing some significant differences from the model without seasonal succession. Moreover, we use a "thin-tail" condition on the kernel function to estimate the asymptotic speeds of (g, h) and the asymptotic spreading speed of u, which is achieved by solving the associated semi-wave problem. [ABSTRACT FROM AUTHOR]

A nonlocal diffusion single population model with advection and free boundaries is considered. Our aim is to discuss how the advection rate affects dynamic behaviors of species under the case of small advection. Firstly, the well-posed global solution is obtained. Secondly, we apply the eigenvalue problem of integro-differential operator to obtain the dichotomy and sharp criteria for spreading and vanishing, which is determined by initial habitat and initial density. Further, the asymptotic spreading speed of species is estimated when spreading happens. Namely, we get the exact asymptotic spreading speed and find that if kernel function satisfies the certain condition, then the leftward asymptotic spreading speed is less than the rightward one due to the impact of advection rate. Meanwhile, we also observe that accelerated spreading happens if the certain condition does not be satisfied. [ABSTRACT FROM AUTHOR]

The evolutionary impact of both temporal periodicity and spatial heterogeneity on population ecology is a challenging problem. Hutson et al. (2001) [12] and Bai et al. (2022) [2] studied the effects of diffusion rates on the dynamics of a time-periodic Lotka-Volterra competition-diffusion system with identical interspecific competition abilities. In this paper, we consider the case of different interspecific competition coefficients. The obtained results can be divided into two groups. The first part focuses on the interplay between the diffusion intensities and the interspecific competition coefficients on the dynamics in the weak competition case. We provide some sufficient conditions on coexistence and competitive exclusion. The second part considers the dynamics for fixed diffusion coefficients and varying competition coefficients. We not only provide a complete classification on the dynamics when one of the interspecific competition coefficients is small, but also show the multiple coexistence periodic patterns by applying the bifurcation method. [ABSTRACT FROM AUTHOR]

The dynamics of a general reaction–diffusion–advection two species model with nonlocal delay effect and Dirichlet boundary condition is investigated in this paper. The existence and stability of the positive spatially nonhomogeneous steady state solution are studied. Then by regarding the time delay τ as the bifurcation parameter, we show that Hopf bifurcation occurs near the steady state solution at the critical values τ n (n = 0 , 1 , 2 , ...) . Moreover, the Hopf bifurcation is forward and the bifurcated periodic solutions are stable on the center manifold. The general results are applied to a Lotka–Volterra competition–diffusion–advection model with nonlocal delay. [ABSTRACT FROM AUTHOR]

The dynamics of the reaction-diffusion-advection population models with linear boundary condition has been widely studied. This paper is devoted to the dynamics of a reaction-diffusion-advection population model with nonlinear boundary condition. Firstly, the stability of the trivial steady state is investigated by studying the corresponding eigenvalue problem. Secondly, the existence and stability of nontrivial steady states are proved by applying the Crandall-Rabinowitz bifurcation Theorem, the Lyapunov-Schmidt reduction method and perturbation method, in which bifurcation from simple eigenvalue and that from degenerate simple eigenvalue are both possible. The general results are applied to a parabolic equation with monostable nonlinear boundary condition, and to a parabolic equation with sublinear growth and superlinear boundary condition. Our theoretical results show that the nonlinear boundary condition can lead to the occurrence of various steady state bifurcations. Meanwhile, compared with the linear boundary condition, the nonlinear boundary condition can induce the multiplicity and growing-up property of positive steady-state solutions for the model with logistic interior growth. Finally, the numerical results show that the advection can change the bifurcation direction of some bifurcation, and affect the density distribution of the species. [ABSTRACT FROM AUTHOR]

In this paper, a reaction–diffusion–chemotaxis HIV-1 model with a cytotoxic T lymphocyte (CTL) immune response and general sensitivity is investigated. We first prove the global classical solvability and L ∞ -boundedness for the considered model in a bounded domain with arbitrary spatial dimensions, which extends the previous existing results. Then, we apply the global existence result to the case with a linear proliferation immune response and an incidence rate. We study the spatiotemporal dynamics about the three types of spatially homogeneous steady states: infection-free steady state S 0 , CTL-inactivated infection steady state S 1 , and CTL-activated infection steady state S ∗. Our analyses indicate that S 0 is globally asymptotically stable if the basic reproduction number R 0 is less than 1; if R 0 is between 1 and a threshold, then S 1 is globally asymptotically stable. However, if R 0 is larger than the threshold, then the chemoattraction and chemorepulsion can destabilize S ∗ , and thus, a spatiotemporal pattern forms as the chemotactic sensitivity crosses certain critical values. We obtain two kinds of important patterns, which are induced by chemotaxis: stationary Turing pattern and irregular oscillatory pattern. We also find that different chemotactic response functions can affect system's dynamics. Based on some empirical parameter values, numerical simulations are given to illustrate the effectiveness of the theoretical predications. [ABSTRACT FROM AUTHOR]

This paper aims to introduce a new multiple attribute decision-making model named possibility Fermatean fuzzy soft set (PFFSS), which is a combination of the generalized fuzzy soft sets and Fermatean fuzzy sets. Some operations and properties of the new model, including complement, restricted union, and extended intersection are discussed. Further, an application of PFFSSs is modeled for multiple attribute decision-making and solved with the help of our newly launched algorithm, that is, the selection of the best eco-system model based on a computer simulation report. Finally, a comparative analysis between the initiated PFFSS model and some existing approaches is provided to show its reliability over them. [ABSTRACT FROM AUTHOR]

The existence, direction and stability of Hopf bifurcating periodic orbits near the positive spatially nonhomogeneous steady state of a reaction–diffusion–advection model with distributed delay and Dirichlet boundary condition are considered in this paper. By analyzing the characteristic equation and taking the bound of time delay as the bifurcation parameter, we show that Hopf bifurcation will occur when the shape parameter n ≥ 1 , and the positive steady state is always stable when n = 0. The properties of Hopf bifurcations are then obtained by center manifold reduction and norm form methods. The effects of the distributed delay, shape parameter and advection on Hopf bifurcation values are also investigated. Finally, numerical simulations illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates a Lotka–Volterra competition model for two species in a one-dimensional habitat that incorporates time delays and free boundaries. The well-posed global solutions are first established by a compatible condition with the initial habitat. On this basis, the long-time behaviors and the spreading–vanishing criteria are elaborated. Furthermore, if the spreading occurs, we estimate the upper and lower bounds of asymptotic spreading speed using delay-induced semi-wave problems. It illustrates that the asymptotic spreading speed cannot be faster than the minimal speed of traveling wavefront solutions corresponding to the Cauchy problem. Besides, the numerical simulations verify the theoretical results and reveal some new phenomena. [ABSTRACT FROM AUTHOR]

In this paper, we consider a diffusive three-species food chain system with strong Allee effect subject to the Neumann boundary condition. The dynamics of the local system including stability of interior equilibria and Hopf bifurcation are discussed. For the diffusive system, we study the existence of non-negative solutions, stability of a positive homogeneous steady state, diffusion-driven Turing instability and the occurrence of Turing–Hopf bifurcation. Employing the multiple scale analysis, we derive the normal form of Turing–Hopf bifurcation, which helps us classify the dynamical behaviors of the diffusive system near the Turing–Hopf bifurcation point. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate a diffusive intraguild predation model with intraspecific competition and double free boundaries in one-dimensional space. By adapting existing techniques, we first prove the existence and uniqueness, regularity and uniform estimates of global solution. Then, in terms of parameters range, we show that a spreading-vanishing dichotomy for this free boundary problem. The long time behaviors of (R , N , P) and criteria for spreading and vanishing are also obtained. Additionally, when spreading happens, we propose an upper bound and a lower bound for the asymptotic spreading speeds of the free boundaries. Moreover, numerical simulations are provided to confirm our theoretical results. This paper is an improvement and extension of literatures [Zhang DW, Dai BX. A free boundary problem for the diffusive intraguild predation model with intraspecific competition. J Math Anal Appl. 2019;474:381–412; Zhang DW, Dai BX. Spreading and vanishing in a diffusive intraguild predation model with intraspecific competition and free boundary. Math Methods Appl Sci. 2019;42:6917–6943]. [ABSTRACT FROM AUTHOR]

We consider the attraction–repulsion chemotaxis system in a smoothly bounded domain Ω ⊆ R 2 . When the system is parabolic–elliptic–parabolic–elliptic, we establish the finite time blow-up conditions of nonradial solutions by making a differential inequality on the moment of solutions. Apart from that, in some special cases, the solutions of the system are globally bounded without blow-up. Our results extend some known conclusions in the literature. [ABSTRACT FROM AUTHOR]

In this paper, a reaction–diffusion SEI epidemic model with nonlinear incidence rate is proposed. The well-posedness of solutions is studied, including the existence of positive and unique classical solution and the existence and the ultimate boundedness of global solutions. The basic reproduction numbers are given in both heterogeneous and homogeneous environments. For spatially heterogeneous environment, by the comparison principle of the diffusion system, the infection-free steady state is proved to be globally asymptotically stable if R 0 < 1 , if R 0 > 1 , the system will be persistent and admit at least one positive steady state. For spatially homogenous environment, by constructing a Lyapunov function, the infection-free steady state is proved to be globally asymptotically stable if R 0 < 1 , and then the unique positive steady state is achieved and is proved to be globally asymptotically stable if R 0 > 1. Finally, two examples are given via numerical simulations, and then some control strategies are also presented by the sensitive analysis. [ABSTRACT FROM AUTHOR]

In this paper, we give a new notion of the picture m-polar fuzzy sets (Pm-PFSs) (i.e, combination between the picture fuzzy sets (PFSs) and the m-polar fuzzy sets (m-PFSs)) and study several of the structure operations including subset, equal, union, intersection, and complement. After that, the basic definitions, theorems, and examples on Pm-PFSs are explained. Also, the certain distance between two Pm-PFSs and a novel similarity measure for Pm-PFSs based on distances are defined. MCDM is animated for Pm-PFS data that take into account the distances for the best alternative (solution) by proposed an application of similarity measure for Pm-PFSs in decision-making. Finally, we construct a new methodology to extend the TOPSIS to Pm-PFS in which capable of different objects recognizing belonging to the same family and illustrate its applicability via a numerical example. [ABSTRACT FROM AUTHOR]

In this paper, we consider a classical two-species Lotka–Volterra competition–diffusion–advection model with time delay effect. By utilizing the implicit function theorem, we obtain the existence of at least one spatially nonhomogeneous positive steady state under some conditions on parameters. By analyzing the corresponding characteristic equation, we show the local stability of this spatially nonhomogeneous positive steady state and the occurrence of Hopf bifurcation from it. When there is no time delay, we also study the global stability of the positive steady state. Based on the idea of Chen et al (2018 J. Differ. Equ. 264 5333–5359), the stability and direction of Hopf bifurcation are derived by introducing a weighted inner product associated with the advection rate. Finally, numerical simulations are carried out to verify the theoretical analysis results. [ABSTRACT FROM AUTHOR]

In this paper, we study the spreading speed and traveling wave of an impulsive reaction–diffusion model with non-monotone birth function and age structure, which models the evolution of annually synchronized emergence of adult population with maturation. Our result is an extension to that recently established in Bai, Lou and Zhao (J. Nonlinear Sci. 2022). Numerical simulations are also performed to illustrate our result. [ABSTRACT FROM AUTHOR]

This paper is concerned with the spreading and vanishing phenomena in a diffusive intraguild (IG) predation model with intraspecific competition and free boundary in one dimensional space. The main objective is to obtain the asymptotic behavior of spread of an invasive or new IG prey species via a free boundary. In two cases, we prove a spreading‐vanishing dichotomy for this model, specifically, the IG prey species either successfully spreads to infinity as t→∞ at the front and survives in the new environment or spreads within a bounded area and dies out in the long run. The long time behavior of (R,N,P) and criteria for spreading and vanishing are also obtained. And then, we estimate the asymptotic spreading speed of the free boundary when spreading happens. Besides, two numerical examples are given to illustrate the impacts of initial occupying area and expanding capability on the free boundary. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we investigate a free boundary problem for the diffusive intraguild predation model with intraspecific competition in one dimensional space. The main objective is to portray the asymptotic behavior of spread of an invasive or new predator species via a free boundary. In this model, we assume both the IG prey and the IG (invasive/new) predator species with intraspecific competition, and the IG predator species can only expand further into the new environment from the right end of the initial region. In both cases, we prove a spreading–vanishing dichotomy for this model, specifically, the IG predator species either successfully spreads to infinity as t → ∞ at the front and survives in the new environment, or spreads within a bounded area and dies out in the long run. The long time behavior of (R , N , P) and criteria for spreading and vanishing are also obtained. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the spatiotemporal pattern formation in a diffusive intraguild predation (IGP) model with a nonlocal interaction term in the growth of the shared resource, which extends previous studies of local reaction-diffusion IGP model. We first perform the stability and Hopf bifurcation analyses for the unique positive equilibrium of the corresponding non-spatial system, and give analytical formulas to determine the direction and stability of the bifurcating periodic solutions. Then the linear stability analysis for the nonlocal model shows that the nonlocal interaction is a key mechanism for the formation of Turing patterns. Numerical simulations show that low conversion rate from resource to IG predator can induce stationary Turing patterns, intermediate conversion rate can induce regular oscillatory patterns, and high conversion rate can induce irregular spatiotemporal chaotic patterns for certain diffusive rate. The impact of nonlocal interaction on the resulting patterns with certain diffusive rate is further explored by numerical simulations, which show that nonlocal interaction can induce pattern transition from stationary Turing patterns to non-stationary oscillatory patterns, and even to spatiotemporal chaotic patterns with the increase of the nonlocal interaction tensity. In addition, spatiotemporal chaotic patterns are found in the Turing-Hopf parametric space, which enrich pattern dynamics for diffusive IGP models with nonlocal interactions. [ABSTRACT FROM AUTHOR]

Abstract The spatiotemporal pattern formation and selection driven by nonlinear cross-diffusion of a toxic-phytoplankton–zooplankton model with Allee effect is investigated in this paper. We first perform the mathematical analysis of the corresponding non-spatial model and spatial model, which give us a complete picture of the global dynamics. Then the linear stability analysis shows that the nonlinear cross-diffusion is the key mechanism for the formation of spatial patterns. By taking cross-diffusion rate as bifurcation parameter, amplitude equations under nonlinear cross-diffusion are derived that describe the spatiotemporal dynamics, which interprets the structural transitions and stability of various forms of Turing patterns. Finally, numerical simulations illustrate the effectiveness of theoretical results. It is shown that the spatiotemporal distribution of the plankton is homogeneous when in the absence of cross-diffusion. However, when the cross-diffusivity is greater than its critical value, the spatiotemporal distribution of all the plankton species becomes inhomogeneous in spaces and results in different kinds of patterns: spot, stripe, and the mixture of spot and stripe depending on the nonlinear cross-diffusivity. Simultaneously, the impact of Allee effect and toxin-producing rate of toxic-phytoplankton species on pattern selection is also explored. [ABSTRACT FROM AUTHOR]

A delayed intraguild predation (IGP) model with intraspecific competition is considered. It is shown that the delay has a destabilizing effect and induces oscillations. The global existence results of periodic solutions bifurcating from the positive equilibrium are established. It is shown that there exists at least one nontrival periodic solution when the delay passes through a certain critical value. Numerical simulations are performed to illustrate our theoretical results and show that intraspecific competition can also affect the stability of the positive equilibrium of the system. [ABSTRACT FROM AUTHOR]

Based on biological meaning, a kind of diffusive intraguild predation (IGP: resource, IG prey and IG predator) model with delay effect is investigated in this paper. The model has Holling-Type I functional response between resource-IG prey and resource-IG predator; Holling-Type II functional response between IG prey and IG predator. We first give sufficient conditions on the stability of possible nonnegative constant steady-state solutions for the proposed model, which give us a complete picture of the global dynamics. Then we investigate Hopf bifurcation near the unique positive constant steady-state solution by taking delay as bifurcation parameter and derive the Hopf bifurcation threshold. It is shown that the delay can induce three types of bistability (node-node bistability, node-cycle bistability and cycle-cycle bistability), periodic oscillations and irregular oscillations triggering spatiotemporal chaos in the diffusive IGP model. Numerical simulations are performed to illustrate our theoretical results and suggest that delay can even trigger the emergence of self-organised spatiotemporal patterns, which evolve from spiral patterns to irregular spatial patterns via spatiotemporal Hopf bifurcation. In addition, the impact of diffusion on the model’s dynamics under certain time delay are also explored. [ABSTRACT FROM AUTHOR]

Spatiotemporal patterns driven by cross-diffusion of a uni-directional consumer-resource (C-R) system with Holling-II type functional response are investigated in this paper. The existence of a unique positive steady state of the considered system is studied first. The linear stability analysis shows that the cross-diffusion is the key mechanism for the formation of spatiotemporal patterns through Turing bifurcation. We choose the cross-diffusion coefficient as bifurcation parameter and discuss three different types of Turing bifurcations, corresponding to simple, double non-resonant and double resonant cases. Based on weakly nonlinear analysis with the multiple scale method and the adjoint system theory, we derive the amplitude equations of the Turing patterns near the Turing bifurcation point and obtain the analytical approximation solutions of the patterns for each case. Specially, some qualitative results of amplitude equations of the resonant case are given in detail. Finally, numerical simulations are performed to illustrate the weakly nonlinear theoretical predictions and through these simulations some patterns (single mode pattern, mixed-mode pattern, super-squares pattern, roll pattern, hexagonal pattern) are found. Simultaneously, numerical simulations show that the resource supplying rate has an important impact on the direction of Turing bifurcation. [ABSTRACT FROM AUTHOR]

The spatiotemporal pattern induced by cross-diffusion of a toxic-phytoplankton-zooplankton model with nonmonotonic functional response is investigated in this paper. The linear stability analysis shows that cross-diffusion is the key mechanism for the formation of spatial patterns. By taking cross-diffusion rate as bifurcation parameter, we derive amplitude equations near the Turing bifurcation point for the excited modes in the framework of a weakly nonlinear theory, and the stability analysis of the amplitude equations interprets the structural transitions and stability of various forms of Turing patterns. Furthermore, we illustrate the theoretical results via numerical simulations. It is shown that the spatiotemporal distribution of the plankton is homogeneous in the absence of cross-diffusion. However, when the cross-diffusivity is greater than the critical value, the spatiotemporal distribution of all the plankton species becomes inhomogeneous in spaces and results in different kinds of patterns: spot, stripe, and the mixture of spot and stripe patterns depending on the cross-diffusivity. Simultaneously, the impact of toxin-producing rate of toxic-phytoplankton (TPP) species and natural death rate of zooplankton species on pattern selection is also explored. [ABSTRACT FROM AUTHOR]

In this paper, we study an SIR epidemic model with birth pulse and pulse vaccination. We present a new constructor method of Poincaré maps. Using this method, we construct a Poincaré map. However, for this Poincaré map, we can’t directly use the bifurcation theorem to discuss the existence of flip bifurcations. We use a new method to investigate the existence of flip bifurcations. We establish that the system undergoes flip bifurcation when the maximum birth rate passes some critical values. Furthermore, some numerical simulations are given to illustrate our results. [ABSTRACT FROM AUTHOR]

We propose a kind of delayed diffusive intraguild predation model with Holling II functional response in this paper. By analyzing the eigenvalue spectrum, it is found that the stability or instability of equilibria can be induced by delay. By utilizing the local bifurcation theory of partial functional differential equations, Hopf bifurcation of the proposed system with time delay as bifurcation parameter is investigated. It reveals that the time delay has a destabilizing effect in the intraguild predation model dynamics and a phenomenon of Hopf bifurcation occurs when the delay increases through a certain threshold. Then we give the explicit formulas to determine the direction, stability of Hopf bifurcation by utilizing the normal form method and center manifold reduction for PFDEs. Numerical simulations are performed to illustrate our theoretical results and show that delay and diffusion can induce the system into chaos and even trigger the emergence of different types of spatial patterns, including spiral wave pattern and chaotic wave pattern, which are induced by Hopf instability. [ABSTRACT FROM AUTHOR]

In this paper, a multi-group SIR epidemic model with nonlocal diffusion and nonlinear incidence rate in spatially heterogeneous environment is proposed. The well-posedness, including the existence, positivity and boundedness of solutions, is achieved. The basic reproduction number R 0 is defined, and the existence of principal eigenvalue is studied. Further, the threshold criteria on the global dynamics of the model are established in terms of R 0. That is, when R 0 < 1 , the disease-free steady state is globally asymptotically stable, when R 0 > 1 , the disease is uniformly persistent. Particularly, a single-group degenerated SIR epidemic model is also studied. We give some properties on the principle eigenvalue and prove that there exists a compact global attractor for the solution semiflow. Furthermore, when the basic reproduction number R ̄ 0 > 1 , we obtain that the endemic steady state is unique to exist and globally asymptotically stable. [ABSTRACT FROM AUTHOR]

An SIR epidemic model with saturated treatment function and nonlinear pulse vaccination is studied. The existence and stability of the disease-free periodic solution are investigated. The sufficient conditions for the persistence of the disease are obtained. The existence of the transcritical and flip bifurcations is considered by means of the bifurcation theory. The stability of epidemic periodic solutions is discussed. Furthermore, some numerical simulations are given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we study a stage structure population model with fixed-time birth pulse and state feedback control strategy. The stability of the trivial solution and the existence of periodic solutions are investigated. Sufficient conditions for the permanence of the system are obtained. Furthermore, some numerical simulations are given to illustrate our results. The superiority of the mixed control strategy is also discussed. [ABSTRACT FROM AUTHOR]

In this paper, a general Kolmogorov type predator–prey model is considered. Together with a constant-yield predator harvesting, the state dependent feedback control strategies which take into account the impulsive harvesting on predators as well as the impulsive stocking on the prey are incorporated in the process of population interactions. We firstly study the existence of an order-1 homoclinic cycle for the system. It is shown that an order-1 positive periodic solution bifurcates from the order-1 homoclinic cycle through a homoclinic bifurcation as the impulsive predator harvesting rate crosses some critical value. The uniqueness and stability of the order-1 positive periodic solution are derived by applying the geometry theory of differential equations and the method of successor function. Finally, some numerical examples are provided to illustrate the main results. These results indicate that careful management of resources and harvesting policies is required in the applied conservation and renewable resource contexts. [ABSTRACT FROM AUTHOR]

This paper deals the two-species chemotaxis system in a smoothly bounded domain Ω ⊂ R n (n ≥ 1). It is proved that the solution of the system is globally bounded and exponentially convergent to the constant steady state solution under small initial conditions ‖ u 0 ‖ L n + β (Ω) and ‖ ω 0 ‖ L n + β (Ω) for any β > 0 , and the convergence rates are calculated accurately. The present work improves the results under small initial conditions ‖ u 0 ‖ L ∞ (Ω) and ‖ ω 0 ‖ L ∞ (Ω) in Tao and Winkler (2015). [ABSTRACT FROM AUTHOR]

In this paper, the dynamics for a class of state-dependent impulsive predator–prey models with the logistic growth for the predator and prey species are analyzed. By a direct calculation, the existence of a semi-trivial periodic solution is obtained. Based on the geometrical analysis and biological background, the strict threshold value conditions for the existence of positive periodic solutions are depicted. The stabilities of the semi-trivial periodic solution and positive order-1 periodic solutions are proved due to the analogue of Poincaré criterion. Numerical results are carried out to illustrate the feasibility of our main results. [ABSTRACT FROM AUTHOR]

We study the existence of periodic solutions for a class of state-dependent impulsive differential systems via geometrical analysis methods. Our results show that these periodic solutions are generated by impulses. Moreover, numerical simulations are used to examine the existence of the periodic solutions. [ABSTRACT FROM AUTHOR]

In this paper we use variational methods to investigate the existence of periodic solutions for some second order delay differential systems with impulsive effects. Some new methods and results are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we consider the existence of solutions for second-order nonlinear damped impulsive differential equations with Dirichlet boundary condition. By critical point theory, we obtain some existence theorems of solutions for the nonlinear problem. We extend and improve some recent results. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a class of damped vibration problems with impulsive effects is considered. An existence result is obtained by using the variational method and the critical point theorem due to Brezis and Nirenberg. The obtained result is also valid and new for the corresponding second-order impulsive Hamiltonian system. Finally, an example is presented to illustrate the feasibility and effectiveness of the result. [ABSTRACT FROM AUTHOR]

In this paper, a class of impulsive damped vibration problems are considered. Existence results are obtained by using variational method and critical point theorem. The obtained results are also valid and new even if the impulsive damped vibration problem is reduced to impulsive Hamiltonian system and Hamiltonian system. Examples are presented to illustrate the feasibility and effectiveness of the results. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a class of second-order impulsive Hamiltonian systems are considered. Some new existence results are obtained by using a variational method and critical point theorem due to Tang and Wu. Some recent results are extended. Three examples are presented to illustrate the feasibility and effectiveness of our results. [Copyright &y& Elsevier]

In this paper, we study the nonlinear Riesz space-fractional convection–diffusion equation over a finite domain in two dimensions with a reaction term. The Crank–Nicolson difference method for the temporal and the weighted–shifted Grünwald–Letnikov difference method for the spatial discretization are proposed to achieve a second-order convergence in time and space. The D'Yakonov alternating–direction implicit technique, which is effective in two–dimensional problems, is applied to find the solution alternatively and reduce the computational cost. The unconditional stability and convergence analyses are proved theoretically. Numerical experiments with their known exact solutions are conducted to illustrate our theoretical investigation. The numerical results perfectly confirm the effectiveness and computational accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a p-Laplacian boundary value problem with impulsive effects is considered. Multiplicity of solutions is obtained by three critical points theorem. An example is presented to illustrate main result. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the existence of solutions for a class of nonlinear impulsive problems with periodic boundary conditions. By using critical point theory, we obtain some existence theorems of infinitely many solutions for the nonlinear impulsive problem when the impulsive functions are superlinear. We extend and improve some recent results. [Copyright &y& Elsevier]

Abstract: This paper investigates the existence of multiple periodic solutions for impulsive Gause-type ratio-dependent predator–prey systems with non-monotonic numerical responses and time delays. Some sufficient conditions are derived by using the continuation theorem of coincidence degree theory and analysis technique. As corollaries, some applications are listed. In particular, the presented criteria improve and extend many previous results in the literature. [Copyright &y& Elsevier]

Abstract: In this paper, an impulsive boundary value problem with a parameter is considered. By using critical point theory, some criteria are obtained to guarantee that the impulsive problem has at least one solution, two solutions and infinitely many solutions when the parameter lies in different intervals. The results obtained are also valid and new for a problem discussed in the literature. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the existence of solutions for a class of nonlinear impulsive problems with Dirichlet boundary conditions. We obtain some new existence theorems of solutions for the nonlinear impulsive problem by using critical point theory. We extend and improve some recent results. [ABSTRACT FROM AUTHOR]

Abstract: Considering the effects of changing environments, delays, impulses and functional response, a one-prey multi-predators system is established in this paper. Using comparison theorem and some analysis techniques, sufficient conditions ensuring the global attractivity of the prey-extinction positive periodic solution and the permanence of the system are obtained. Finally, examples and numerical simulations are given to show the effectiveness of the main results. [Copyright &y& Elsevier]