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This paper is concerned with the propagation phenomenon of a three species predation-competition system with nonlocal dispersal and climate change effects. That is to say, there is not only competition for food, but also competitive interaction between two preys. The growth rate of each prey is nondecreasing along the $ x $-axis and shifts rightward at a speed $ s $. We mainly consider the population dynamics for three cases: (ⅰ) the predator spreads faster than the two preys, (ⅱ) the predator spreads between two preys and (ⅲ) the predator with slower speed spreads behind the two preys, including multiple layers with different speeds to achieve a complete picture. Due to lack of comparison principle in the prey-predator system and compactness of the nonlocal operator, we give some priori estimates of the solutions to obtain the persistence for three species, which depends on improving the regularity of the dispersal kernels and proposing some parameter conditions of the considered system. [ABSTRACT FROM AUTHOR]

This paper is concerned with the propagation phenomena for a nonlocal dispersal Lotka–Volterra competition model with shifting habitats. It is assumed that the growth rate of each species is nondecreasing along the x-axis, positive near ∞ and nonpositive near - ∞ , and shifting rightward with a speed c > 0 . In the case where both species coexist near ∞ , we established three types of forced waves connecting the origin, respectively to the coexistence state with any forced speed c; to itself with forced speed c > c ∗ (∞) ; and to a semi-trivial steady state with forced speed c > c ¯ (∞) , where c ∗ (∞) and c ¯ (∞) are two positive numbers. In the case where one species is competitively stronger near ∞ , we also obtain the existence and nonexistence of forced waves connecting the origin to the semi-trivial steady state. Our results show the existence of multiple types of forced waves with the same forced speed. The mathematical proofs involve integral equations and Schauder's fixed point theorem, and heavily rely on the construction of various upper-lower solutions, which adds new techniques to deal with the "shifting environments" problem. [ABSTRACT FROM AUTHOR]

This paper is concerned with the propagation dynamics of nonlocal dispersal monostable equations in time-space periodic habitats. We first show that such an equation admits a single spreading speed in every direction under certain conditions and then give several spreading properties in terms of spreading speeds such as asymptotic spreading ray speeds and asymptotic spreading sets. Furthermore, we consider the dependence of the spreading speed on the dispersal rate and reaction term and prove that taking the temporal average or spatial average can decrease the spreading speed. Finally, we employ the viscosity vanishing method to establish the existence of time-space periodic traveling fronts with the critical speed in every direction under the partially temporally homogeneous case and partially nearly flat case, which solves partially the open problem raised by Rawal, Shen, and Zhang (Discrete Contin. Dyn. Syst. 35 (2015) 1609–1640). [ABSTRACT FROM AUTHOR]

In this paper, we study the spreading properties of a nonlocal dispersal reducible cooperation model under a shifting habitat. By considering the corresponding upper and lower control systems, we find that the left and right expansion fronts of the solutions with exponentially unbounded kernels propagate with finite speed and infinite speed, respectively. This is quite different from the case of exponentially bounded kernels (Wang and Li, 2020), in which the expansion fronts of the solutions always spread to the left and right with finite speeds. That is to say, we have found a new phenomenon that linear extension and accelerating propagation appear at the same time for such a system. [ABSTRACT FROM AUTHOR]

In this paper, we study a Lotka–Volterra cooperative system with nonlocal dispersal under worsening habitats. By constructing appropriate vector super-/subsolutions combined with the monotone iteration scheme, we obtain the existence of bounded and positive forced waves connecting zero equilibrium to the coexistence state of the limiting system corresponding to the most favorable resource with the wave speed at which the habitat is worsening. Compared with the existence result of traveling wave to the homogeneous system, we find that the wave phenomenon is more likely to occur in such shifting environment. Here, we remove the common assumption that the dispersal kernels are compactly supported and symmetric. Further, we investigate the tail behavior of the forced waves, especially for the rate of convergence to the extinction state, and derive the long-time dynamics of two species. Our result shows that weak interspecies cooperation and nonlocal diffusion pattern cannot prevent species from disappearing eventually under such a worsening habitat. [ABSTRACT FROM AUTHOR]

Recently, the spreading speeds and periodic traveling wave solutions for a general class of partially degenerate nonlocal dispersal cooperative systems in time and space periodic habitats have been investigated. In this paper, we continue to study the stability and convergence rate for such time and space periodic traveling waves. We show that if the initial function perturbation is uniformly bounded with respect to a weighted maximum norm, the periodic traveling wave solution is globally exponentially stable when the wave speed is greater than the spreading speed. [ABSTRACT FROM AUTHOR]