Search

In this paper, we deal with the global dynamics of a Lotka-Volterra competition-diffusion-advection system with nonlinear boundary conditions, including the existence, nonexistence and global stability of coexistence steady states. We start with the investigation of the principal eigenvalue of linearized system to get the local stability of steady states and then discuss the global dynamics in terms of competition coefficients. [ABSTRACT FROM AUTHOR]

This paper is concerned with an integral equation that models discrete time dynamics of a population in a patchy landscape. The patches in the domain are reflected through the discontinuity of the kernel of the integral operator at a finite number of points in the whole domain. We prove the existence and uniqueness of a stationary state under certain assumptions on the principal eigenvalue of the linearized integral operator and the growth term as well. We also derive criteria under which the population undergoes extinction (in which case the stationary solution is 0 everywhere). [ABSTRACT FROM AUTHOR]

Temperature-dependent sex determination (TSD) is an environmental phenomenon in which the temperature during the embryonic or larval stages influences the determination of sex. It is mainly observed in teleost fish, where high water temperatures can induce a female-to-male transition. The exact mechanism by which environmental changes affect TSD is poorly understood, but cortisol, a stress hormone, is considered a potential factor. Although excessive secretion of cortisol is known to cause side effects, it can lead to a switch in sex hormones, potentially resulting in TSD. In this paper, we investigate the mechanism of TSD in teleost fish. To assess the impact of stress caused by changes in water temperature on TSD, we established a mathematical model for hormonal dynamics that incorporates cortisol. First, we conducted a stability analysis to qualitatively examine the sex determination. The temperature dependence was modeled using the Eyring–Polanyi equation, and we examined corresponding hormonal changes with water temperature. Furthermore, we theoretically investigated the role of a cortisol inhibitor in preventing side effects during TSD. [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]

In this paper, the author focuses on the joint effects of diffusion and advection on the dynamics of a classical two species Lotka-Volterra competition-diffusion-advection system, where the ratio of diffusion and advection rates are supposed to be a positive constant. For comparison purposes, the two species are assumed to have identical competition abilities throughout this paper. The results explore the condition on the diffusion and advection rates for the stability of former species. Meanwhile, an asymptotic behavior of the stable coexistence steady states is obtained. [ABSTRACT FROM AUTHOR]

Complex metapopulation dynamics research has a profound impact on our understanding of the relationship between species and their habitats. In this paper, the dynamical behaviors of the single-species metapopulation model with reproductive and reaction time delays based on Levins’ model are investigated by analyzing stability charts, rightmost characteristic roots, and bifurcation diagrams of the positive equilibrium. Finally, the theoretical results are compared with the numerical results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a predator–prey model with nonuniform predator dispersal, called predation-induced dispersal (PID), which represents predator motility depending on the maximal predation rate and the predator death rate in a spatially heterogeneous region. We study the local stability of the semitrivial steady state when predators are absent for models with PID and linear dispersal. We then investigate the local/global bifurcation from the semitrivial steady state of these models. Finally, we compare the results of the model with PID to the results of the model with linear dispersal. We conclude that the nonuniform dispersal of predators obeying PID increases fitness for predator invasion when rare; thus, predators with PID can invade a region with an increased probability even in cases wherein predators dispersed linearly cannot invade a certain region. Based on the results, we provide an ecological interpretation with the simulations. [ABSTRACT FROM AUTHOR]

This paper is devoted to the existence, multiplicity, stability, and Hopf bifurcation of steady-state solutions of a diffusive Lotka–Volterra type model for two species with nonlocal delay effect and nonlinear boundary condition. It is found that there is no Hopf bifurcation when the interior reaction term is weaker than the boundary reaction term, and that the interior reaction delay determines the existence of Hopf bifurcation only when the interior reaction term is stronger than the boundary reaction term. This observation helps us to understand the nonlinear balance between the interior reaction and boundary flux in nonlinear boundary problems. Moreover, the general results are illustrated by applications to a model with homogeneous kernels. [ABSTRACT FROM AUTHOR]

Multi-strain diseases lead to the development of some degree of cross-immunity among people. In the present paper, we propose a multi-delayed SIRC epidemic model with incubation and immunity time delays. Here we aim to examine and investigate the effects of incubation delay (τ 1) and the impact of vaccine which provides partial/cross-immunity with immunity delay parameter ( τ 2 ) on the disease dynamics. Also, we study the impact of the strength of cross-immunity (σ) on the disease prevalence. The positivity and boundedness of the solutions of the epidemic model have been established. Two different types of equilibrium points (disease-free and endemic) have been deduced. Expression for basic reproduction number has been derived. The stability conditions and Hopf-bifurcation about both the equilibrium points in the absence and presence of both delays have been discussed. The Lyapunov stability conditions about the endemic equilibrium point have been established. Numerical simulations have been performed to support our analytical results. We quantitatively demonstrate how oscillations and Hopf-bifurcation allow time delays to alter the dynamics of the system. The combined impacts of both the delays on disease prevalence has been studied. Through parameter sensitivity analysis, we observe that the infected population decreases with an increase in vaccination rate and the system starts to stabilize early with the increase in cross-immunity rate. Global sensitivity analysis for the basic reproduction number has been performed using Latin hypercube sampling and partial rank correlation coefficients techniques. The combined effect of vaccination rate with transmission rate and vaccination rate with re-infection probability (i.e. strength of cross-immunity) on R 0 have been discussed. Our research underlines the need to take cross-immunity and time delays into account in the epidemic model in order to better understand disease dynamics. [ABSTRACT FROM AUTHOR]

The time-delayed Moran-Ricker population model is investigated in this paper with an aim to identify some of its unknown features. In this model, the decline of the essential resources arising from the previous generation emerges as a delay in the density dependency of the population. The random fluctuations in population size may cause the model’s dynamics to change. In this study, we aim to scrutinize the model thoroughly and reveal more properties of the model. A discussion about the fixed points and their stability is presented in a brief way. By studying the normal form of the model through the reduction of the model to the associated center manifold, we show that the model will experience flip (period-doubling), Neimark–Sacker, strong resonances, and period-doubling-Neimark Sacker bifurcations. The bifurcation conditions are extracted with their critical coefficients. Numerical bifurcation analysis confirms the validity of theoretical findings. [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]

Lotka–Volterra (LV) equations play a key role in the mathematical modeling of various ecological, biological and chemical systems. When the number of species (or, depending on the viewpoint, chemical components) becomes large, basic but fundamental questions such as computing the number of surviving species still lack theoretical answers. In this paper, we consider a large system of LV equations where the interactions between the various species are a realization of a random matrix. We provide conditions to have a unique equilibrium and present a heuristics to compute the number of surviving species. This heuristics combines arguments from Random Matrix Theory, mathematical optimization (LCP), and standard extreme value theory. Numerical simulations, together with an empirical study where the strength of interactions evolves with time, illustrate the accuracy and scope of the results. [ABSTRACT FROM AUTHOR]

In this paper, we develop a method of analyzing long transient dynamics in a class of predator–prey models with two species of predators competing explicitly for their common prey, where the prey evolves on a faster timescale than the predators. In a parameter regime near a singular zero-Hopf bifurcation of the coexistence equilibrium state, we assume that the system under study exhibits bistability between a periodic attractor that bifurcates from the singular Hopf point and another attractor, which could be a periodic attractor or a point attractor, such that the invariant manifolds of the coexistence equilibrium point play central roles in organizing the dynamics. To find whether a solution that starts in a vicinity of the coexistence equilibrium approaches the periodic attractor or the other attractor, we reduce the equations to a suitable normal form, and examine the basin boundary near the singular Hopf point. A key component of our study includes an analysis of the long transient dynamics, characterized by their rapid oscillations with a slow variation in amplitude, by applying a moving average technique. We obtain a set of necessary and sufficient conditions on the initial values of a solution near the coexistence equilibrium to determine whether it lies in the basin of attraction of the periodic attractor. As a result of our analysis, we devise a method of identifying early warning signals, significantly in advance, of a future crisis that could lead to extinction of one of the predators. The analysis is applied to the predator–prey model considered in Sadhu (Discrete Contin Dyn Syst B 26:5251–5279, 2021) and we find that our theory is in good agreement with the numerical simulations carried out for this model. [ABSTRACT FROM AUTHOR]

In this paper, we propose a diffusive prey-predator model with saturated hunting cooperation and predator-taxis. We first establish the global classical solvability and boundedness, and provide some sufficient conditions to assure the existence of a unique positive homogeneous steady state and the global uniform asymptotic stability of the predator-free homogeneous steady state. Secondly, we study the pattern formation mechanism and reveal that pattern formation is driven by the joint effect of predator-taxis, hunting cooperation, and slow diffusivity of predators. Moreover, we find that a strong predator-taxis can annihilate the spatiotemporal patterns, but a weak predator-taxis supports the pattern formation when diffusion-driven instability is present in the model without predator-taxis. However, if diffusion-driven instability is absent, predator-taxis cannot destabilize the unique positive spatially homogeneous steady state. Additionally, we highlight that spatially heterogeneous steady states do not exist when the diffusion coefficient ratio of predators to prey is sufficiently large under specific parametric conditions. To explore the various types of spatially heterogeneous steady states, we derive amplitude equations based on the weakly nonlinear analysis theory. Finally, numerical simulations, including the hexagonal pattern, stripe pattern, a mixed pattern combining hexagons and stripes, and the square pattern, are presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we study a three-patch two-species Lotka–Volterra competition patch model over a stream network. The individuals are subject to both random and directed movements, and the two species are assumed to be identical except for the movement rates. The environment is heterogeneous, and the carrying capacity is lager in upstream locations. We treat one species as a resident species and investigate whether the other species can invade or not. Our results show that the spatial heterogeneity of environment and the magnitude of the drift rates have a large impact on the competition outcomes of the stream species. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the asymptotic dynamics of a time-periodic parasitic–mutualistic model of mistletoes and birds in heterogeneous environment with the especial concerns over the spreading–vanishing scenarios, in which the Stefan class free boundary is introduced as the spreading frontier. By defining the ecological reproduction number and generalizing it as the spatial-temporal risk index, a considerably universal spreading–vanishing dichotomy and the sharp criteria are first established in birds world in the absence of mistletoes, and some estimates of the asymptotic spreading speed of the free boundary provided that spreading occurs are also obtained. Furthermore, the comprehensive considerations containing the spreading frontiers, asymptotic profiles and estimates of the asymptotic spreading speed are exhibited in mistletoes-birds world by the monotone iteration technique with the proper upper and lower solutions. The results suggest that even for the spreading case, the mistletoes population will eventually persist in long term provided that its own risk index is larger than 1, otherwise it may be eradicated. [ABSTRACT FROM AUTHOR]

We study a Lotka–Volterra competition–diffusion model that describes the growth, spread and competition of two species in a shifting habitat. Some results have been obtained previously for some cases for the diffusion rates and competitions rates, and in this paper we continue to explore the remaining complementary case for the spatial dynamics of the system. Our main result in this paper reveals an essential difference between the case of faster diffuser being weak competitor and the case of faster diffuser being strong competitor: with the severe habitat worsening with constant speed, for the former the two competing species can co-persist by spreading, whereas for the latter, co-persistence is impossible. [ABSTRACT FROM AUTHOR]

It is well known that in reaction-diffusion models for a single unstructured population in a bounded, static, heterogeneous environment, slower diffusion is advantageous. That is not necessarily the case for stage structured populations. In (Cantrell et al. 2020), it was shown that in a stage structured model introduced by Brown and Lin (1980), there can be situations where faster diffusion is advantageous. In this paper we extend and refine the results of (Cantrell et al. 2020) on persistence to more general combinations of diffusion rates and to cases where either adults or juveniles do not move. We also obtain results on the asymptotic behavior of solutions as diffusion rates go to zero, and on competition between species that differ in their diffusion rates but are otherwise ecologically identical. We find that when the spatial distributions of favorable habitats for adults and juveniles are similar, slow diffusion is still generally advantageous, but if those distributions are different that may no longer be the case. [ABSTRACT FROM AUTHOR]

The decreasing tiger population in the world ecosystem is a threat to nature conservation. Canine distemper virus (CDV) is a deadly virus found in the tiger worldwide, one of the vital causes of their extinction. This paper figure outs the influence of CDV on tiger populations. We have developed and studied a delayed eco-epidemiological tiger-dog/wild carnivores predator-prey model with CDV infection in tiger and dog/wild carnivores considering incubation delay τ for CDV infected dogs and wild carnivores. We studied the existence, boundedness, stability, and bifurcation of the solutions. Our analysis shows that the coexistence equilibrium is locally stable for all incubation delay τ > τ + . The system switches its stability as incubation delay crosses its critical value τ = τ + , perceives oscillations, and Hopf bifurcation occurs in the system for all τ < τ + . Further, the disease-free equilibrium also shows Hopf bifurcation for predator's mortality rate threshold value μ 2 = μ 2 ∗ . We have performed a sensitivity analysis and identified the impact of the system's parameters on reproduction number through their sensitivity indices. Finally, numerical simulation verifies the analytical finding that the significant incubation delay causes stability in the system. We can get a disease-free environment and save tigers by regulating the predation rate of healthy prey(dog/wild carnivores). [ABSTRACT FROM AUTHOR]

Concerned in this paper is a discrete predator-prey system with Allee effect and other food resources for the predators. The conditions on the existence and stability of fixed points are obtained. It is shown that the system can undergo fold bifurcation and flip bifurcation by using the center manifold theorem and bifurcation theory. Numerical simulations are provided to illustrate the feasibility of the main results and the influence of Allee effect on the stability of the system. Our study indicates that other food resources for the predator can enrich the dynamical behaviours of the system, including cascades of period-doubling bifurcation in orbits of period-2, 4, 8, and chaotic sets. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new two-sex mosquito population suppression model including stage structure and a reproduction delay. Sterile mosquitoes are introduced to suppress the development of wild mosquito populations and a special function M s (t) is used as a control function to describe the number of sterile mosquitoes in the field. Firstly, the dynamic behaviors of the system when the control function is a constant function, a general continuous function and a periodic pulse function are analyzed theoretically, and the existence and stability of the equilibria of the system are determined. In particular, the conditions for the global stability of the wild mosquito-extinction equilibrium, that is, the conditions for the successful suppression of wild mosquitoes, are found. Then, a series of numerical simulations are carried out which on the one hand verify the theoretical results obtained, and on the other hand supplement the imperfections of the theoretical study. Finally, a brief conclusion is given, and the focus of further research is pointed out. [ABSTRACT FROM AUTHOR]

In a recent paper by one of the authors and collaborators, motivated by the Olive Quick Decline Syndrome (OQDS) outbreak, which has been ongoing in Southern Italy since 2013, a simple epidemiological model describing this epidemic was presented. Beside the bacterium Xylella fastidiosa, the main players considered in the model are its insect vectors, Philaenus spumarius, and the host plants (olive trees and weeds) of the insects and of the bacterium. The model was based on a system of ordinary differential equations, the analysis of which provided interesting results about possible equilibria of the epidemic system and guidelines for its numerical simulations. Although the model presented there was mathematically rather simplified, its analysis has highlighted threshold parameters that could be the target of control strategies within an integrated pest management framework, not requiring the removal of the productive resource represented by the olive trees. Indeed, numerical simulations support the outcomes of the mathematical analysis, according to which the removal of a suitable amount of weed biomass (reservoir of Xylella fastidiosa) from olive orchards and surrounding areas resulted in the most efficient strategy to control the spread of the OQDS. In addition, as expected, the adoption of more resistant olive tree cultivars has been shown to be a good strategy, though less cost-effective, in controlling the pathogen. In this paper for a more realistic description and a clearer interpretation of the proposed control measures, a spatial structure of the epidemic system has been included, but, in order to keep mathematical technicalities to a minimum, only two players have been described in a dynamical way, trees and insects, while the weed biomass is taken to be a given quantity. The control measures have been introduced only on a subregion of the whole habitat, in order to contain costs of intervention. We show that such a practice can lead to the eradication of an epidemic outbreak. Numerical simulations confirm both the results of the previous paper and the theoretical results of the model with a spatial structure, though subject to regional control only. [ABSTRACT FROM AUTHOR]

Predation can both reduce prey abundance directly (through density-dependent effects) and indirectly through prey trait-mediated effects. Over the years, many studies have focused on describing the density-area relationship (DAR). However, the mechanisms responsible for the DAR are not well understood. Loss and fragmentation of habitats, owing to human activities, creates landscape-level spatial heterogeneity wherein patches of varying size, isolation and quality are separated by a human-modified “matrix” of varying degrees of hostility and has been a primary driver of species extinctions and declining biodiversity. How matrix hostility in combination with trait-mediated effects influence DAR, minimum patch size, and species coexistence remains an open question. In this paper, we employ a theoretical spatially explicit predator–prey population model built upon the reaction-diffusion framework to explore effects of predator-induced emigration (trait-mediated emigration) and matrix hostility on DAR, minimum patch size, and species coexistence. Our results show that when trait-mediated response strength is sufficiently strong, ranges of patch size emerge where a nonlinear hump-shaped prey DAR is predicted and other ranges where coexistence is not possible. In a conservation perspective, DAR is crucial not only in deciding whether we should have one large habitat patch or several-small (SLOSS), but for understanding the minimum patch size that can support a viable population. Our study lends more credence to the possibility that predators can alter prey DAR through predator-induced prey dispersal. [ABSTRACT FROM AUTHOR]

Due to the role of cytoplasmic incompatibility (CI), releasing Wolbachia-infected male mosquitoes into the wild becomes a very promising strategy to suppress the wild mosquito population. When developing a mosquito suppression strategy, our main concerns are how often, and in what amount, should Wolbachia-infected mosquitoes be released under different CI intensity conditions, so that the suppression is most effective and cost efficient. In this paper, we propose a mosquito population suppression model that incorporates suppression and self-recovery under different CI intensity conditions. We adopt the new modeling idea that only sexually active Wolbachia-infected male mosquitoes are considered in the model and assume the releases of Wolbachia-infected male mosquitoes are impulsive and periodic with period T. We particularly study the case where the release period is greater than the sexual lifespan of the Wolbachia-infected male mosquitoes. We define the CI intensity threshold, mosquito release thresholds, and the release period threshold to characterize the model dynamics. The global and local asymptotic stability of the origin and the existence and stability of T-periodic solutions are investigated. Our findings provide useful guidance in designing practical release strategies to control wild mosquitoes. [ABSTRACT FROM AUTHOR]

Identifying early warning signs of sudden population changes and mechanisms leading to regime shifts are highly desirable in population biology. In this paper, a two-trophic ecosystem comprising of two species of predators, competing for their common prey, with explicit interference competition is considered. With proper rescaling, the model is portrayed as a singularly perturbed system with fast prey dynamics and slow dynamics of the predators. In a parameter regime near singular Hopf bifurcation, chaotic mixed-mode oscillations (MMOs), featuring concatenation of small and large amplitude oscillations are observed as long-lasting transients before the system approaches its asymptotic state. To analyze the dynamical cause that initiates a large amplitude oscillation in an MMO orbit, the model is reduced to a suitable normal form near the singular-Hopf point. The normal form possesses a separatrix surface that separates two different types of oscillations. A large amplitude oscillation is initiated if a trajectory moves from the “inner” to the “outer side” of this surface. A set of conditions on the normal form variables are obtained to determine whether a trajectory would exhibit another cycle of MMO dynamics before experiencing a regime shift (i.e. approaching its asymptotic state). These conditions serve as early warning signs for a sudden population shift as well as detect the onset of a regime shift in this ecological model. [ABSTRACT FROM AUTHOR]

Invasive pest establishment is a pervasive threat to global ecosystems, agriculture, and public health. The recent establishment of the invasive spotted lanternfly in the northeastern United States has proven devastating to farms and vineyards, necessitating urgent development of population dynamical models and effective control practices. In this paper, we propose a stage-age-structured system of PDEs to model insect pest populations, in which underlying dynamics are dictated by ambient temperature through rates of development, fecundity, and mortality. The model incorporates diapause and non-diapause pathways, and is calibrated to experimental and field data on the spotted lanternfly. We develop a novel moving mesh method for capturing age-advection accurately, even for coarse discretization parameters. We define a one-year reproductive number ( R 0 ) from the spectrum of a one-year solution operator, and study its sensitivity to variations in the mean and amplitude of the annual temperature profile. We quantify assumptions sufficient to give rise to the low-rank structure of the solution operator characteristic of part of the parameter domain. We discuss establishment potential as it results from the pairing of a favorable R 0 value and transient population survival, and address implications for pest control strategies. [ABSTRACT FROM AUTHOR]

This paper is concerned with spreading phenomena of the classical two-species Lotka-Volterra reaction-diffusion system in the weak competition case. More precisely, some new sufficient conditions on the linear or nonlinear speed selection of the minimal wave speed of travelling wave fronts, which connect one half-positive equilibrium and one positive equilibrium, have been given via constructing types of super-sub solutions. Moreover, these conditions for the linear or nonlinear determinacy are quite different from that of the minimal wave speeds of travelling wave fronts connecting other equilibria of Lotka-Volterra competition model. In addition, based on the weighted energy method, we give the global exponential stability of such solutions with large speed $c$. Specially, when the competition rate exerted on one species converges to zero, then for any $c>c_0$ , where $c_0$ is the critical speed, the travelling wave front with the speed $c$ is globally exponentially stable. [ABSTRACT FROM AUTHOR]

In this paper, we use an integrodifference equation model and pairwise invasion analysis to find what dispersal strategies are evolutionarily stable strategies (also known as evolutionarily steady or ESS) when there is spatial heterogeneity and possibly seasonal variation in habitat suitability. In that case there are both advantages and disadvantages of dispersing. We begin with the case where all spatial locations can support a viable population, and then consider the case where there are non-viable regions in the habitat. If the viable regions vary seasonally, and the viable regions in summer and winter do not overlap, dispersal may really be necessary for sustaining a population. Our findings generally align with previous findings in the literature that were based on other modeling frameworks, namely that dispersal strategies associated with ideal free distributions are evolutionarily stable. In the case where only part of the habitat can sustain a population, we show that a partial occupation ideal free distribution that occupies only the viable region is associated with a dispersal strategy that is evolutionarily stable. As in some previous works, the proofs of these results make use of properties of line sum symmetric functions, which are analogous to those of line sum symmetric matrices but applied to integral operators. [ABSTRACT FROM AUTHOR]

This paper is concerned with the spatially periodic Fisher–KPP equation u t = (d (x) u x) x + (r (x) - u) u , x ∈ R , where d(x) and r(x) are periodic functions with period L > 0 . We assume that r(x) has positive mean and d (x) > 0 . It is known that there exists a positive number c d ∗ (r) , called the minimal wave speed, such that a periodic traveling wave solution with average speed c exists if and only if c ≥ c d ∗ (r) . In the one-dimensional case, the minimal speed c d ∗ (r) coincides with the "spreading speed", that is, the asymptotic speed of the propagating front of a solution with compactly supported initial data. In this paper, we study the minimizing problem for the minimal speed c d ∗ (r) by varying r(x) under a certain constraint, while d(x) arbitrarily. We have been able to obtain an explicit form of the minimizing function r(x). Our result provides the first calculable example of the minimal speed for spatially periodic Fisher–KPP equations as far as the author knows. [ABSTRACT FROM AUTHOR]

This paper is concerned with the time periodic traveling wave solutions for a periodic Lotka–Volterra predator–prey system, which formulates that both species synchronously invade a new habitat. We first establish the existence of periodic traveling wave solutions by combining the upper and lower solutions with contracting mapping principle and Schauder's fixed point theorem. The asymptotic behavior of nontrivial solution is given precisely by the stability of the corresponding kinetic system that has been widely investigated. Then, the nonexistence of periodic traveling wave solutions is confirmed by applying the theory of asymptotic spreading. We show the conclusion for all positive wave speed and obtain the minimal wave speed. [ABSTRACT FROM AUTHOR]

Our earlier work in Nguyen et al. (Maximizing metapopulation growth rate and biomass in stream networks. arXiv preprint , 2023) shows that concentrating resources on the upstream end tends to maximize the total biomass in a metapopulation model for a stream species. In this paper, we continue our research direction by further considering a Lotka–Volterra competition patch model for two stream species. We show that the species whose resource allocations maximize the total biomass has the competitive advantage. [ABSTRACT FROM AUTHOR]

Phytoplankton is an important indicator organism to evaluate the quality of water environment, which may reflect the nutritional level of the sea area. Conversely, environmental conditions can directly affect the community structure of phytoplankton. A stochastic phytoplankton–zooplankton model considering non-degenerate and degenerate diffusions is formulated in this paper. What’s more, in both systems, we obtain sufficient conditions of extinction and ergodicity. Our results demonstrate that the weaker white noise can ensure the permanence of zooplankton and the stronger white noise can lead to the disappearance of zooplankton. Moreover, the threshold value of extinction and persistence can serve as a theoretical basis for controlling phytoplankton and zooplankton. Numerical examples are performed on the analysis results of the two cases to confirm our theoretical results. In addition, we also provide a real-life case study, the validity of the model is verified based on experimental data, and it is shown that fluctuation of external environment and the consumption of phytoplankton by zooplankton will affect the growth and number of phytoplankton. Effectively controlling the quantity of phytoplankton can delay the occurrence of water bloom or red tide. [ABSTRACT FROM AUTHOR]

In this paper, we study a three-dimensional stochastic vegetation–water model in arid ecosystems, where the soil water and the surface water are considered. First, for the deterministic model, the possible equilibria and the related local asymptotic stability are studied. Then, for the stochastic model, by constructing some suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution ϖ (·) . In a biological interpretation, the existence of the distribution ϖ (·) implies the long-term persistence of vegetation under certain conditions. Taking the stochasticity into account, a quasi-positive equilibrium D ¯ ∗ related to the vegetation-positive equilibrium of the deterministic model is defined. By solving the relevant Fokker–Planck equation, we obtain the approximate expression of the distribution ϖ (·) around the equilibrium D ¯ ∗ . In addition, we obtain sufficient condition R 0 E < 1 for vegetation extinction. For practical application, we further estimate the probability of vegetation extinction at a given time. Finally, based on some actual vegetation data from Wuwei in China and Sahel, some numerical simulations are provided to verify our theoretical results and study the impact of stochastic noise on vegetation dynamics. [ABSTRACT FROM AUTHOR]

In this paper, we consider a two-predator–one-prey population model that incorporates both the inter-specific competition between two predator populations and the intra-specific competition within each predator population. We investigate the dynamics of this model by addressing the existence, local and global stability of equilibria, uniform persistence as well as saddle-node and Hopf bifurcations. Numerical simulations are presented to explore the joint impacts of inter-specific and intra-specific competition on competition outcomes. Though inter-specific competition along does not admit a stable coexistence equilibrium, with intra-specific competition, the coexistence of the two competing predator species becomes possible and the two coexisting predator species may maintain at two different equilibrium populations. [ABSTRACT FROM AUTHOR]

To cope with the problems existing in the education and Management of students in traditional colleges and universities, improve the management efficiency and realize the informatization of education management, this study proposes a set of optimization paths for the education and Management of students in colleges and universities. In this paper, an intelligent and diversified education management platform is constructed, aiming to strengthen the operation efficiency of the education management team in colleges and universities. By introducing a fuzzy evaluation algorithm to judge the educational management paths of college students and normalizing the input data, empirical evaluation results are derived. Comparative Analysis of the data in the study showed that the optimized educational management path significantly improved students’ daily behavior and mental health status. Students’ average daily online time was effectively controlled between 5.6 and 10.5 hours, the online period was more in line with the healthy work and rest, and the rates of disciplinary behaviors and Internet fraud victimization decreased respectively. At the same time, students’ mental health and learning effects were also improved. In summary, the education and management path for college students proposed in this paper significantly strengthens the management system and comprehensively cultivates students. It provides an effective informatization strategy for education management in colleges and universities.

The present paper is devoted to the investigation of population dynamics under climate change. The evolution of species is modelled by a reaction-diffusion equation in a spatio-temporally heterogeneous environment described by a climate envelope that shifts with a time-dependent speed function. For a general almost-periodic speed function, we establish the persistence criterion in terms of the sign of the approximate top Lyapunov exponent and, in the case of persistence, prove the existence of a unique forced wave solution that dominates the population profile of species in the long run. In the setting for studying the effects of fluctuations in the shifting speed or location of the climate envelope, we show by means of matched asymptotic expansions and numerical simulations that the approximate top Lyapunov exponent is a decreasing function with respect to the amplitude of fluctuations, yielding that fluctuations in the shifting speed or location have negative impacts on the persistence of species, and moreover, the larger the fluctuation is, the more adverse the effect is on the species. In addition, we assert that large fluctuations can always drive a species to extinction. Our numerical results also show that a persistent species under climate change is invulnerable to mild fluctuations, and becomes vulnerable when fluctuations are so large that the species is endangered. Finally, we show that fluctuations of amplitude less than or equal to the speed difference between the shifting speed and the critical speed are too weak to endanger a persistent species. [ABSTRACT FROM AUTHOR]

In this paper, we propose a diffusive competition model with habitat degradation and homogeneous Neumann boundary conditions in a bounded domain that is partitioned into the healthy region (undisturbed habitat) and the degraded region (due to anthropogenic habitat disturbance). Species follow the Lotka-Volterra competition in the healthy region while in the degraded region species experience only exponential decay (not necessarily at the same rate). This setup is novel in that it requires no positivity assumption on the environmental heterogeneity, either absolute or on average, which would be far too restrictive for the study of the effects of habitat degradation. We rigorously show competitive exclusion and coexistence via global stability analysis. A remarkable finding is that the quality heterogeneity of landscapes can lead to the competitive exclusion of the slower species by the faster species. This result is robust as long as the degraded region has positive area, and moreover is at odds with classical results predicting the deterministic extinction of the stronger species. On the other hand, if the degraded region has intermediate negative effect on the faster competitor, species can coexist. Differing from comparable existing results, coexistence does not rely on a limit as the diffusion coefficients tend to zero or infinity. Together, these results imply that coexistence is always a possibility under this basic, yet general, configuration, providing insights into the varying impacts found through empirical study of habitat loss and fragmentation on species. [ABSTRACT FROM AUTHOR]

In this paper, we study a reaction-diffusion system under homogeneous Dirichlet boundary conditions that describes the evolution of population densities of a mutualist–prey species u, a predator species v and a mutualist species w. Firstly, stability properties of the trivial and semi-trivial solutions are determined completely. It is found that when the (local) stability of trivial and semi-trivial solutions change, positive stationary solutions appear and the appropriate expressions of these solutions are derived. Furthermore, we show that for large γ , there is at most one positive stationary solution for each fixed b ∈ R , moreover it is asymptotically stable (if it exists). Our results indicate that the dynamics of the predator–prey–mutualist system is much complicated than that of the classic predator–prey system. [ABSTRACT FROM AUTHOR]

This work is concerned with competitive Lotka–Volterra model with Markov switching. A novelty of the contribution is that the Markov chain has a countable state space. Our main objective of the paper is to reduce the computational complexity by using the two-time-scale systems. Because existence and uniqueness as well as continuity of solutions for Lotka–Volterra ecosystems with Markovian switching in which the switching takes place in a countable set are not available, such properties are studied first. The two-time scale feature is highlighted by introducing a small parameter into the generator of the Markov chain. When the small parameter goes to 0, there is a limit system or reduced system. It is established in this paper that if the reduced system possesses certain properties such as permanence and extinction, etc., then the complex system also has the same properties when the parameter is sufficiently small. These results are obtained by using the perturbed Lyapunov function methods. [ABSTRACT FROM AUTHOR]

Several mathematical models are proposed to understand spatial patchy vegetation patterns arising in drylands. In this paper, we consider the system with nonlocal dispersal of plants (through a redistribution kernel for seeds) proposed by Pueyo et al. (Oikos 117:1522-1532, 2008) as a model for vegetation in water-limited ecosystems. It consists in two reaction diffusion equations for surface water and soil water, combined with an integro-differential equation for plants. For this system, under suitable assumptions, we prove well-posedness using the Schauder fixed point theorem. In addition, we consider the stationary problem from the viewpoint of vegetated pattern formation, and show a transition of vegetation patterns when parameter values (rainfall, seed dispersal range, seed germination rate) in the system vary. The influence of the shape of the redistribution kernel is also discussed. [ABSTRACT FROM AUTHOR]