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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 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]

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]

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]

In this paper, a predator-prey model with double Allee effects and impulse is studied. The existence and stability of the prey-free periodic solution are investigated. The sufficient conditions for global stability of the prey-free periodic solution are obtained. We also find a critical threshold that the predator and prey populations will coexist. The existence of the transcritical bifurcations is considered by means of the bifurcation theory when the prey population is not subject to Allee effect. Combining mathematical analysis and numerical simulations, we show that the double Allee effects and impulse greatly alter the outcome of the survival of both species. [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]

Parameters in ecological models are often known to be imprecise. In this paper, we consider a two-species competition fishery model with interval-valued species specific growth rates and interspecies competition parameters. Conditions involving the lower and upper bounds of the model imprecise parameters are derived for extinction and coexistence of two competing species. Existence of bionomic equilibria and optimal harvesting policies are also discussed. Numerical simulations based on Monte Carlo method are performed to address biological implications of our findings. [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, we consider the existence and multiplicity of solutions for a class of nonlinear impulsive problem on the half-line. By using a variational method and a variant fountain theorem, we obtain some new criteria to guarantee that the impulsive problem has at least one solution and infinitely many solutions respectively. We extend and improve some recent results. [ABSTRACT FROM AUTHOR]

By using Mawhin continuation theorem and constructing suitable Lyapunov functional, a set of easily verifiable sufficient conditions ensuring the existence and global asymptotical stability of positive periodic solutions for two-species non-autonomous diffusion competition n-patch system with time delay and impulses are established. Finally, applications and an illustrative example are given. The main results generalize and improve the previously known results in Zhang and Wang (J. Math. Anal. Appl. 265:38-48, ), Dong et al. (Chaos Solitons Fractals 32:1916-1926, ). [ABSTRACT FROM AUTHOR]

River network morphology not only reflects the structure of river stream but also has great effects on hydrological process, soil erosion, river evolution, and watershed topography. Here we propose and define a new sequence of self-similar networks and corresponding parameters for the generated Tokunaga network. We also discuss the topological and numerical characteristics of self-similar networks with different iteration rules by utilizing links and fractal dimension. Application results indicate that the proposed method could be used to generate river network, which is much consistent with natural river network. The proposed parameter λ could well reflect the river network morphology. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a discrete-time non-autonomous predator-prey system with the Beddington-DeAngelis functional response. By using the coincidence degree and the related continuation theorem as well as some priori estimates, easily verifiable sufficient criteria are established for the existence of positive periodic solutions. [ABSTRACT FROM AUTHOR]

It is well known that the drug treatment is always combined with the injection of immune factors. In this paper, a virus infection model with state-dependent impulsive control is considered. Firstly, by deriving three categories of Bendixson domain and using the methods of geometry and successor function, we establish some criteria for the existence of positive order-1 periodic solution for a general model, which extends the existing results in the literature. Further, the criteria are used to obtain the existence of positive order-1 periodic solutions in the two cases that the positive equilibrium point is on the left or right side of the pulse line, respectively. Finally, an example is presented to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we study a delayed predator-prey model with impulse and, in particular, the existence of the predator-free periodic solution. We employ the approach and techniques coming from epidemiology and calculate the basic reproduction number for the predator. Using the basic reproduction number, we consider the global attraction of the predator-free periodic solution and uniform persistence of the predator. Our results improve the results by Li and Liu (Adv. Differ. Equ. 2016:42, 2016), where they left the open problem of finding a threshold value that determines the eradication and uniform persistence of the predator. Furthermore, we give some numerical simulations to illustrate our results. [ABSTRACT FROM AUTHOR]

A three-species cooperative system with time delays and Lévy jumps is proposed in this paper. Firstly, by comparison method and inequality techniques, we discuss the stability in mean and extinction of species, and the stochastic permanence of this system. Secondly, by applying asymptotic method, we investigate the stability in distribution of solutions. Thirdly, utilizing ergodic method, we obtain the optimal harvesting policy of this system. Finally, some numerical examples are given to illustrate our main results. [ABSTRACT FROM AUTHOR]

In this paper, we propose a host-vector-predator model with stage structure for the vector to explore the impact of biological control agents on host-vector dynamics and disease control. Here the total vector population is divided into two physiological subclasses which are immature and mature subclasses. Holling type II functional response is used to portray the interactions between vectors and predators. Stability analysis of the equilibria demonstrates that the basic reproduction number gives the threshold condition determining the persistence and extinction of the disease. Furthermore, the phenomenon of Hopf bifurcation occurs when predators are introduced. The stability of limit cycle arising from a Hopf bifurcation is rigorously investigated. Finally, numerical simulations are given to show the validity of analytical results, and the comparative results of disease dynamics with and without predators. [ABSTRACT FROM AUTHOR]