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This paper presents new criteria for the oscillation of all solutions of the third-order nonlinear delay differential equations with noncanonical operators. Our approach to establishing new criteria essentially simplifies and refines the main results obtained in Džurina and Jadlovská (2018) and Grace et al. (2019). Examples illustrating the importance of our results are presented. • This paper presents new criteria for the oscillation of all solutions of the third-order nonlinear delay differential equations with noncanonical operators. We first transform the studied nonlinear noncanonical third-order delay differential equation into semi-canonical type. This approach simplifies the examination of the considered equation. Moreover, our approach to establishing new criteria substantially improves and extends some known results in the relevant literature. [ABSTRACT FROM AUTHOR]

The motivation of this paper is inspired by the research of Zanette et al. (2011) [4] , which reveals that the perception of predation risk can reduce the number of juvenile prey. To investigate how fear affects the behavior of prey population, we formulate a predator-prey model with a stage structure for prey in which adult prey is undergoing the interference of fear. First, the dynamic properties of the model are analyzed, including the existence and stability of equilibria, bifurcations dynamics, such as transcritical, saddle-node, and Hopf bifurcations. Our results reveal that fear can promote the formation of the stability of the model by transforming it from an unstable state to a stable state. Numerical simulations and theoretical analysis indicated that when the level of fear reaches 25.4, the number of juvenile prey affected by fear decreases by 40% compared to those not affected by fear. Terrifyingly, the predators are on the brink of extinction in high levels of fear. Moreover, we examine the impact of time delay on fear in the previous model as prey needs some time to assess the predation risk. Some dynamic characteristics of this delayed model are also analyzed. Results indicate that the fear effect is conducive to generating a stable state, while delay is detrimental to generating a stable state, leading to limit cycles or even chaos. • A stage-structure predator-prey model with fear and delay is proposed. • The feasibility equilibria and bifurcation dynamics of the model are studied. • Fear can transform a model from an unstable state to a stable state. • Delay is detrimental to generating a stable state, leading to limit cycles or chaos. [ABSTRACT FROM AUTHOR]

This paper examines a class of two-species reaction-diffusion-advection competition models with two time delays. A system of DDE equations was derived, both theoretically and numerically, using the Galerkin technique method. A condition is defined that helps to find the existence of Hopf bifurcation points. Full diagrams of the Hopf bifurcation points and areas of stability are investigated in detail. Furthermore, we discuss three different sources of delay on bifurcation maps, and what impacts of all these cases of delays on others free rates on the regions of the Hopf bifurcation in this model. We find two different stability regions when the delay time is positive (τ > 0), while the no-delay case (τ = 0) has only one stable region. Moreover, the effect of delays and diffusion rates on all free others parameters in this model have been considered, which can significantly impact upon the stability regions in both population concentrations. It is also found that, as diffusion increases, the time delay increases. However, as the delay maturation is increased, the Hopf points for both proliferation of the population and advection rates are decreased and it causes raises to the region of instability. In addition, bifurcation diagrams are drawn to display chosen instances of the periodic oscillation and two dimensional phase portraits for both concentrations have been plotted to corroborate all analytical outputs that investigated in the theoretical part. • To study the effect of diffusion with two different delay terms on the two-species advection competition system. • To drive theoretical outcomes of the DDE obtainable utilizing the Galerkin technique tool. • To find, theoretically, a condition that assists to obtain the existence of Hopf bifurcation points. • To construct the bifurcation diagram for the DDE and DPDE systems via numerical simulation to confirm theoretical results. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we propose the split-step theta method for stochastic delay integro-differential equations by the Lagrange interpolation technique and investigate the mean square exponential stability of the proposed scheme. It is shown that the split-step theta method can inherit the mean square exponential stability of the continuous model under the linear growth condition and the proposed stability condition by the delayed differential and difference inequalities established in the paper. A numerical example is given at the end of the paper to illustrate the method and conclusion of the paper. In addition, the convergence of the split-step theta method is proved in the Appendix. [ABSTRACT FROM AUTHOR]

Abstract In this paper, for the first time, fractional Taylor–Jumarie series expansion is used to solve a glass of time-fractional delay partial differential equation by piecewise interpolation reproducing kernel method (RKM), this class of equations describe sand motion model in beach formation. The aim of this work is to obtain more accurate numerical solution by fractional Taylor–Jumarie series expansion and piecewise interpolation technique. Three numerical experiments are provided to show the advantage of this method, the results show the characteristics of sand motion. The research in this paper is the theoretical basis for further sand motion study. [ABSTRACT FROM AUTHOR]

In this paper, we propose a social contagion model with group interactions on heterogeneous network, in which the group interactions are represented by incorporating higher-order terms. The dynamics of the proposed model are analyzed, revealing the effect of group interactions on the system dynamics. We derive a global asymptotically stability condition of the zero equilibrium point. If the parameters enhancement factor and transform probability meet the condition, the social contagion will eventually disappear. The bifurcation behavior arising from group interactions is investigated, when the enhancement factor exceeds a threshold, the system undergoes a backward bifurcation. This implies that R 0 < 1 does not guarantee the disappearance of social contagion, we also need to control the initial values of social contagion at a lower level. The optimal control strategies for the model are provided. Moreover, the numerical simulations validate the accuracy of the theoretical analysis. It is worth noting that the group interactions lead to the emergence of a bistable phenomenon, in which the social contagion will either fade away or persist eventually, depending on the initial values. • The simplicial SIS social contagion model with delay is proposed on heterogeneous networks. • The dynamics of the model are analyzed, revealing the effect of group interactions on the system dynamics. • An optimal control strategy is proposed for the model, incorporating group interactions. [ABSTRACT FROM AUTHOR]

Abstract: The stabilization of a class of Hamiltonian systems with state time-delay and input saturation is addressed in this paper. Sufficient conditions are derived by using Lyapunov–Krasovskii functional theorem to guarantee the systems as well as the resulted closed-loop systems by output feedback to be asymptotically stable when input saturation effectively occurs. A numerical example is presented to illustrate the effectiveness of the obtained results in this paper. [Copyright &y& Elsevier]

Abstract: In this paper, we will establish some new oscillation criteria for second order quasi-linear neutral delay differential equations of the form The results obtained essentially improve and extend those of Dzurina and Stavroulakis [J. Dzurina, I.P. Stavroulakis, Oscillation criteria for second-order delay differential equations, Appl. Math. Comput. 140 (2003) 445–453], Sun and Meng [Y.G. Sun, F.W. Meng, Note on the paper of Dzurina and Stavroulakis, Appl. Math. Comput. 174 (2006) 1634–1641]. [Copyright &y& Elsevier]

Oscillation criteria are obtained by using the so called H-method for the second order neutral type delay differential equations of the form(r(t)ψ(x(t))z′(t))′+q(t)f(x(σ(t)))=0, t&ges;t0,where z(t)=x(t)+p(t)x(τ(t)), r, p, q, τ, σ, ∈C([t0,∞),R) and f,ψ∈C(R,R).The results of the paper contains several results obtained previously as special cases. Furthermore, we are also able to fix an error in a recent paper related to the oscillation of second order nonneutral delay differential equations. [Copyright &y& Elsevier]

The paper considers a generalized Dickman equation t x ˙ ( t ) = − ∑ i = 1 s a i x ( t − τ i ) for t  → ∞ where s ∈ N , a i  > 0, τ i  > 0, i = 1 , … , s and ∑ i = 1 s a i = 1 . It is proved that there are two mutually disjoint sets of positive decreasing solutions such that, for every two solutions from different sets, the limit of their ratio for t  → ∞ equals 0 or ∞. The asymptotic behavior of such solutions is derived and a structure formula utilizing such solutions and describing all the solutions of a given equation is discussed. In addition, a criterion is proved giving sufficient conditions for initial functions to generate solutions falling into the first or the second set. Illustrative examples are given. Some open problems are suggested to be solved. [ABSTRACT FROM AUTHOR]

• The existence and the uniqueness of mild solutions of random integrodifferential equations are studied • We develop a new tool in the resolvent operator theory and apply several fixed-point theorems • We establish the properties of mean-square stability and attractiveness • We apply the theoretical outcomes to a type of the Heath-Jarrow-Morton-Musiela (HJMM) equation In this paper, the existence and the uniqueness of mild solutions of random integrodifferential equations are studied. To obtain random solutions, we develop a new tool in the resolvent operator theory and apply several fixed-point theorems. In addition, we establish the properties of mean-square stability and attractiveness. In the end, examples are worked out and we apply the theoretical outcomes to a type of the Heath-Jarrow-Morton-Musiela (HJMM) equation. [ABSTRACT FROM AUTHOR]

This paper is concerned with traveling waves for n -species competitive Lotka–Volterra system with nonlocal dispersals and delays. Existence of traveling waves which connect the trivial equilibrium and the positive equilibrium indicates that there is a transition zone moving the steady state with no species to the steady state with the coexistence of n -species. In order to obtain the result, we first investigate the general theory for the general systems with the nonlocal dispersals by using Schauder’s fixed point theorem. Numerical simulations are carried out to illustrate the main theoretical results. The work obtained can be seen as a generalization of previous results. [ABSTRACT FROM AUTHOR]

In this paper, a fitted reproducing kernel is proposed for solving singularly perturbed initial value problems. Based on it, an effective numerical method is proposed for a class of singularly perturbed delay initial value problem. Numerical results show that the present reproducing kernel is superior to the usual reproducing kernel for solving singularly perturbed initial value problems. [ABSTRACT FROM AUTHOR]

This paper is concerned with the oscillation of certain third-order nonlinear delay differential equations with damping. We give new characterizations of oscillation of the third-order equation in terms of oscillation of a related, well-studied, second-order linear differential equation without damping. We also establish new oscillation results for the third-order equation by using the integral averaging technique due to Philos. Numerous examples are given throughout. [ABSTRACT FROM AUTHOR]

This paper proposes and investigates a delayed model for the dynamics and control of a mosquito population which is subject to an integrated strategy that includes pesticide release, the use of mechanical controls and the use of the sterile insect technique (SIT). The existence of positive equilibria is characterized in terms of two threshold quantities, being observed that the “richer” equilibrium (with more mosquitoes in the aquatic phase) has better chances to be stable, while a longer duration of the aquatic phase has the potential to destabilize both equilibria. It is also found that the stability of the trivial equilibrium appears to be mostly determined by the value of the maturation rate from the aquatic phase to the adult phase. A nonstandard finite difference (NSFD) scheme is devised to preserve the positivity of the approximating solutions and to keep consistency with the continuous model. The resulting discrete model is transformed into a delay-free model by using the method of augmented states, a necessary condition for the existence of optimal controls then determined. The particularities of different control regimes under varying environmental temperature are investigated by means of numerical simulations. It is observed that a combination of all three controls has the highest impact upon the size of the aquatic population. At higher environmental temperatures, the oviposition rate is seen to possess the most prominent influence upon the outcome of the control measures. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the existence of ω -periodic solutions for second-order functional differential equation with delay in E − u ′ ′ ( t ) = f ( t , u ( t ) , u ( t − τ ) ) , t ∈ R , where E is an ordered Banach space, f : R × E × E → E is a continuous function which is ω -periodic in t and τ ≥ 0 is a constant. We first build a new maximum principle for the ω -periodic solutions of the corresponding linear equation with delay. With the aid of this maximum principle, under the assumption that the nonlinear function is quasi-monotonicity, we study the existence of the minimal and maximal periodic solutions for abstract delayed equation by combining perturbation method and monotone iterative technique of the lower and upper solutions. [ABSTRACT FROM AUTHOR]

This paper investigates the exponential stability and exponential estimate of the norms of solutions to a linear system of difference equations with single delay x ( k + 1 ) = A x ( k ) + B x ( k − m ) , k = 0 , 1 , … where A, B are square constant matrices and m ∈ N . Sufficient conditions for exponential stability are derived using the method of Lyapunov functions and its efficiency is demonstrated by examples. [ABSTRACT FROM AUTHOR]

This paper is concerned with the convergence and asymptotic stability of semidiscrete and full discrete schemes for linear parabolic equations with delay. These full discrete numerical processes include forward Euler, backward Euler and Crank–Nicolson schemes. The optimal convergence orders are consistent with those of the original parabolic equation. It is proved that the semidiscrete scheme, backward Euler and Crank–Nicolson full discrete schemes can unconditionally preserve the delay-independent asymptotic stability, but some additional restrictions on time and spatial stepsizes of the forward Euler full discrete scheme is needed to preserve the delay-independent asymptotic stability. Numerical experiments illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a delayed diffusive predator–prey model with herd behavior. Firstly, by choosing the appropriate bifurcation parameter, the stability of the positive equilibria and the existence of Hopf bifurcations, induced by diffusion and delay respectively, are investigated by analyzing the corresponding characteristic equation. Then, applying the normal form theory and the center manifold argument for partial functional differential equations, the formula determining the properties of the Hopf bifurcation are obtained. Furthermore, the instability of the Hopf bifurcation leads to the emergence of spatial patterns. Finally, some numerical simulations are also carried out to illustrate and expand the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a class of second order nonlinear impulsive delay differential equations with damping term is studied. Three factors-impulse, delay and damping that affect the interval qualitative properties of solutions of equations are taken into account together. Several interval oscillation criteria which generalize some known ones, such as, in Huang and Feng (2010), Xing and Zheng (2008) and Liu and Xu (2007), are established. Moreover, examples are also given to illustrate the effectiveness and non-emptiness of our results. [ABSTRACT FROM AUTHOR]

• We introduce a class of stochastic delay differential equations with delayed impulses and inputs. • The input-to-state stability is studied for two cases where the continuous stochastic delay system is stable and unstable. • Different from the traditional methods, we use the average dwell time and the vector Lyapunov function method. • Two examples are used to verify the validity of our theory results. In this paper, we study the input-to-state stability of a class of stochastic delay differential equations with delay impulses. We consider the two cases where the continuous stochastic delay system is stable and unstable, and establish different types of stability conditions by using the average dwell time and the vector Lyapunov function method. Finally, two examples are used to verify the validity of our results. [ABSTRACT FROM AUTHOR]

In this paper, we use a modification of Krasnoselskii's fixed point theorem introduced by Burton (2002) (see [6] Theorem 3) to obtain stability results of the zero solution of the totally nonlinear neutral differential equations with functional delay x′(t)=-a(t)h(x(t-τ(t)))+d/dtQ(t,x(t-τ(t)))+G(t,x(t-τ(t))). The stability of the zero solution of this equation provided that h(0)=Q(t,0)=G(t,0,0)=0. The Caratheodory condition is used for the functions Q and G. [ABSTRACT FROM AUTHOR]

The aim of this paper is to characterize some parameters which measure the "force of discount" in a discounting function (the instantaneous discount rate and the geometric mean of a discounting function), and relate them with the strong subadditivity and the so-called subadditivity of second order. We distinguish two intertemporal choice frameworks, depending on the consideration of time as an interval or both as an interval and a delay, and we establish some necessary and sufficient conditions to identify strongly subadditive and subadditive of second order discounting functions. [ABSTRACT FROM AUTHOR]

This paper presents the analysis of behavior of stochastic Gompertz model with delay. We prove existence and uniqueness of the global positive solution of the considered model. Besides, the conditions for species to be persistent are established, as well as the conditions under which population becomes extinct. Finally, numerical illustration with real life example is carried out to confirm our theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: Since many systems such as quantum system, complex-valued neural network and Lorenz system are complex-valued differential system, in this paper, the stability of complex-valued impulsive system with delay is addressed. By taking advantage of Lyapunov function in complex field, some new criteria for global exponential stability are established, which not only generalize some known results in literature but also greatly reduce the complexity of analysis and computation. As an application, a new impulsive controller for complex-valued Lü system with delay is designed. [Copyright &y& Elsevier]

Abstract: In this paper, two types of stochastic Lotka–Volterra systems (i.e., competition system and predator–prey system) with time delays and Lévy noise are discussed. For each model, we establish sufficient and necessary criteria for stability in time average and extinction of each population. The thresholds between stability in time average and extinction of each model are obtained. Some recent results are improved and extended significantly. These results point out that: (i) time delays are harmless for stability in time average and extinction of our model; (ii) both stability in time average and extinction have close relationships with Lévy noise; (iii) the interaction rates play significant roles in determining the stability in time average and extinction of the populations. [Copyright &y& Elsevier]

Abstract: In this paper, we consider an almost periodic discrete logistic equation with delay. By constructing suitable Lyapunov functional and almost periodic functional hull theory, a sufficient condition is obtained for the existence of a unique almost periodic solution which is globally attractive. An example together with its numerical simulation shows the feasibility of our main result. [Copyright &y& Elsevier]

Abstract: In this paper, we study a predator–prey model with a transmissible disease spreading in the predator population and a time delay representing the gestation period of the predator. By analyzing corresponding characteristic equations, the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the disease-free equilibrium and the coexistence equilibrium are established, respectively. By means of Lyapunov functionals and LaSalle’s invariance principle, sufficient conditions are derived for the global stability of the predator-extinction equilibrium and the disease-free equilibrium and the global attractiveness of the coexistence equilibrium of the system, respectively. Numerical simulations are carried out to support the theoretical analysis. [Copyright &y& Elsevier]

Abstract: An autonomous stage-structured predator–prey system (stage structure for both predator and prey) with discrete delay is studied in this paper. By using an iterative method, the global stability of the interior equilibrium point of the system is investigated. Our result shows that conditions which ensure the permanence of the system are enough to ensure the global stability of the system. The result not only improves but also complements some existing ones. [Copyright &y& Elsevier]

Abstract: This paper is devoted to a two-species periodic Gause-type ratio-dependent predator–prey system with time delay in a two-patch environment. By using the comparison theorem of differential equations, we establish sufficient conditions for the permanence of the system. As corollaries, some applications are listed. In particular, our results generalize and improve some known ones. [Copyright &y& Elsevier]

Abstract: A stage-structured predator–prey system (stage structure for both predator and prey) with discrete delay is studied in this paper. By introducing a new lemma and applying the standard comparison theorem, a set of novel criteria which ensure the permanence of the system is obtained. Our result supplements the main results of Chen, Xie and Li [Partial survival and extinction of a delayed predator–prey model with stage structure, Applied Mathematics and Computation, 219 (8) (2012) 4157–4162]. [Copyright &y& Elsevier]

Abstract: In this paper, we revisit the non-persistent property of a stage-structured predator–prey system which was proposed by Ma et al. (2008) [Z.H. Ma, Z.Z. Li, S.F. Wang, T.Li, F.P. Zhang, Permanence of a predator–prey system with stage structure and time delay, Appl. Math. Comput. 201 (2008) pp. 65–71]. By applying the standard comparison theorem, some novel results concern with the extinction of the system and partial survival of the predator (prey) species, respectively, are obtained. One of the interesting finding is that for this system, the extinction of prey may not necessarily lead to extinction of predator. [Copyright &y& Elsevier]

Abstract: In this paper, a delayed differential equation model that describes infection of thymus with HIV-1 is considered. We first investigate the existence and stability of the equilibria and then we study the effect of the time delay on the stability of the infected equilibrium. Criteria are given to ensure that the infected equilibrium is asymptotically stable for all delay. Finally, by using a delay as a bifurcation parameter, the existence of Hopf bifurcation is investigated. Numerical simulations are presented to illustrate the analytical results. [Copyright &y& Elsevier]

Abstract: In this paper, we study a delayed six-dimensional human immunodeficiency virus (HIV) model with Cytotoxic T Lymphocytes (CTLs) immune response. Our model describes the interaction of HIV with two target cells: CD4+ T cells and macrophages. We derive that the global asymptotic attractivity of the model is completely determined by the basic reproduction number and the immune reproduction number for the viral infection. By constructing Lyapunov functionals, we have shown that the infection-free equilibrium , the immune-free equilibrium and the chronic-infection equilibrium are globally asymptotically attractive when and , respectively. [Copyright &y& Elsevier]

Abstract: In this paper, we establish some new Gronwall–Bellman-type delay dynamic inequalities on time scales, which can be used as a handy tool in the investigation of qualitative as well as quantitative analysis of solutions of delay dynamic equations on time scales. Our results generalize the main results of Ou-Iang [L. Ou-Iang, The boundedness of solutions of linear differential equations y″+ A(t)y =0, Shuxue Jinzhan 3 (1957) 409-415], Jiang [F.C. Jiang, F.W. Meng, Explicit bounds on some new nonlinear integral inequality with delay, J. Comput. Appl. Math. 205 (2007) 479-486.] and Yuan [Z.L. Yuan, X.W. Yuan, F.W. Meng, Some new delay integral inequalities and their applications, Appl. Math. Comput. 208 (2009) 231-237]. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a delay differential equations model of plankton allelopathy. Using an iterative method, the global stability of the interior equilibrium point of the system is investigated, which shows that toxic substances are harmless for the stability of the interior equilibrium point. The results we obtained improve and complement those of Chattopadhyay [J. Chattopadhyay, Effect of toxic substances on a two-species competitive system, Ecol. Model. 84 (1996) 287–289], Samanta [G.P. Samanta, A two-species competitive system under the influence of toxic substances, Appl. Math. Comput. 216 (2010) 291–299] and Mukhopadhyay et al. [A. Mukhopadhyay, J. Chattopadhyay, P.K. Tapaswi, A delay differential equations model of plankton allelopathy, Math. Biosci. 149 (1998) 167–189]. We also present some examples to verify our main result. [Copyright &y& Elsevier]

Abstract: In this paper, we establish some new oscillation criteria for the following forced functional differential equationNo restriction is imposed on the forcing term e(t) to be the nth derivative of an oscillatory function. Two cases have been taken into consideration: (i) and ; (ii) q(t) changes its sign, 0< λ <1 and . The main results generalize some existing results and can be applied to the oscillation problem that are not covered in the literature. [Copyright &y& Elsevier]

Abstract: This paper is devoted to impulsive periodic Gause-type predator–prey systems with monotonic or non-monotonic numerical responses. With the help of a continuation theorem based on coincidence degree theory, we establish easily verifiable criteria for the existence of positive periodic solutions. As corollaries, some applications are listed. In particular, our results improve and generalize some known ones. [Copyright &y& Elsevier]

Abstract: This paper presents retarded integral inequalities of Henry–Gronwall type. Applying these inequalities, we study certain properties of solutions to fractional differential equations with delay. [Copyright &y& Elsevier]

Abstract: This paper is concerned with upper bounds for the distances between adjacent zeros of solutions of first-order linear delay differential equations with variable coefficients of the form where τ >0 and p(t)∈ C([t ∗,∞), R). By introducing a sequence of testing functions, we are able to derive upper bounds that are better than those in the literature. [Copyright &y& Elsevier]

Abstract: In this paper, a competitive Lotka–Volterra system with three delays is investigated. By choosing the sum of three delays as a bifurcation parameter, we show that in the above system, Hopf bifurcation at the positive equilibrium can occur as crosses some critical values. And we obtain the formulae determining direction of Hopf bifurcation and stability of the bifurcating periodic solutions by using the normal form theory and center manifold theorem. Finally, numerical simulations supporting our theoretical results are also included. [Copyright &y& Elsevier]

Abstract: We are concerned with delay-independent asymptotic stability of linear system of neutral differential equations. We first establish a sufficient and necessary condition for the system to be delay-independently asymptotically stable, and then give some equivalent stability conditions. This paper improves many recent results on the asymptotic stability in the literature. One example is given to show that the sufficient and necessary condition is easy to verify. [Copyright &y& Elsevier]

Abstract: In this paper, we analyze the dynamics of a delayed predator–prey system in the presence of harvesting. This is a modified version of the Leslie–Gower and Holling-type II scheme. The main result is given in terms of local stability, global stability, influence of harvesting and bifurcation. Direction of Hopf bifurcation and the stability of bifurcating periodic solutions are also studied by using the normal form method and center manifold theorem. [Copyright &y& Elsevier]

Abstract: This paper studies the H-infinity control issue for a class of networked control systems (NCSs) with time delay and packet dropout. The state feedback closed-loop NCS is modeled as a discrete-time switched system. Through using a Lyapunov function, a sufficient condition is obtained, under which the system is exponential stability with a desired H-infinity disturbance attenuation level. The designed H-infinity controller is obtained by solving a set of linear matrix inequalities. An illustrative example is presented to demonstrate the effectiveness of the proposed method. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a Timoshenko system with a delay term in the feedback and prove a stability result. The beam is clamped at the endpoints and has, in addition to an internal damping, a feedback with a delay. Under an appropriate assumption on the weights of the two feedbacks, we prove the well-posedness of the system and establish an exponential decay result for the case of equal-speed wave propagation. [Copyright &y& Elsevier]

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]

Abstract: In this paper, we propose a periodic delayed two-species system modeling facultative mutualism. By using the method of coincidence degree and Lyapunov functional, easily verifiable sufficient conditions for the existence and globally asymptotic stability of positive periodic solutions of the above system. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study the difference equation: where . We give some sufficient conditions which guarantee that all solutions of the equation are oscillatory, or that the positive equilibrium of the equation is globally asymptotically stable. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, it is studied that two species predator–prey Lotka–Volterra type dispersal system with delay and Holling type II response function, in which the prey species can disperse among n patches, while the density-independent predator species is confined to one of the patches and cannot disperse. Sufficient conditions of integrable form for the boundedness, permanence, extinction and the existence of positive periodic solution are established, respectively. [Copyright &y& Elsevier]

Abstract: In this paper, Hopf bifurcation for a delayed SIS epidemic model with stage structure and nonlinear incidence rate is investigated. Through theoretical analysis, we show the positive equilibrium stability and the conditions that Hopf bifurcation occurs. Applying the normal form theory and the center manifold argument, we derive the explicit formulas determining the properties of the bifurcating periodic solutions. In addition, we also study the effect of the inhibition effect on the properties of the bifurcating periodic solutions. To illustrate our theoretical analysis, some numerical simulations are also included. [Copyright &y& Elsevier]