Lotka-Volterra Competition Model Research Articles

Temperature Shapes Ecological Dynamics in Mixed Culture Fermentations Driven by Two Species of the Saccharomyces Genus.

Mixed culture wine fermentations combining species within the Saccharomyces genus have the potential to produce new market tailored wines. They may also contribute to alleviating the effects of climate change in winemaking. Species, such as S. kudriavzevii, show good fermentative properties at low temperatures and produce wines with lower alcohol content, higher glycerol amounts and good aroma. However, the design of mixed culture fermentations combining S. cerevisiae and S. kudriavzevii species requires investigating their ecological interactions under cold temperature regimes. Here, we derived the first ecological model to predict individual and mixed yeast dynamics in cold fermentations. The optimal model combines the Gilpin-Ayala modification to the Lotka-Volterra competitive model with saturable competition and secondary models that account for the role of temperature. The nullcline analysis of the proposed model revealed how temperature shapes ecological dynamics in mixed co-inoculated cold fermentations. For this particular medium and species, successful mixed cultures can be achieved only at specific temperature ranges or by sequential inoculation. The proposed ecological model can be calibrated for different species and provide valuable insights into the functioning of alternative mixed wine fermentations.

The path to a 2025 nuclear-free Taiwan: An analysis of dynamic competition among emissions, energy, and economy

Taiwan intends to be nuclear free by 2025. This study employs the Lotka–Volterra competition model for sustainable development to analyze the emissions–energy–economy (3Es) issue to make appropriate policy suggestions for a nuclear-free transition. It also offers a new approach to naming the 3E relationship. The literature review shows that the environmental Kuznets curve accompanies the feedback and conservation hypotheses. In the 3E dynamics relationship analysis, the model shows a good mean absolute percentage error (<15%) for the model estimation. The key findings are as follows: 1) the fossil fuel-led economy exists; 2) CO2 emissions are reduced with nuclear energy consumption; 3) renewable energy is far from scale; 4) a complementary effect exists between fossil fuel and nuclear energy consumption; and 5) gas retrofitting and phasing out of nuclear seem imminent. In the energy transition, Taiwan drastically cuts nuclear energy without considering energy diversity due to which troubles might ensue. The priority issue for Taiwan’s energy mix is energy security. To deal with these concerns, this study suggests the government could improve energy efficiency, build a smart grid, develop carbon capture and storage, and reconsider putting nuclear energy back into the energy mix before renewable energy is scaled.

Global stability of nonhomogeneous equilibrium solution for the diffusive Lotka–Volterra competition model

A diffusive Lotka-Volterra competition model is considered for the combined effect of spatial dispersal and spatial variations of resource on the population persistence and exclusion. First it is shown that in a two-species system in which the diffusion coefficients, resource functions and competition rates are all spatially heterogeneous, the positive equilibrium solution is globally asymptotically stable when it exists. Secondly the existence and global asymptotic stability of the positive and semi-trivial equilibrium solutions are obtained for the model with arbitrary number of species under the assumption of spatially heterogeneous resource distribution. A new Lyapunov functional method is developed to prove the global stability of a non-constant equilibrium solution in heterogeneous environment.

Stability switching curves in a Lotka–Volterra competition system with two delays

This study is devoted to consider the dynamic properties of a Lotka–Volterra competition model with two discrete delays. First, it reviews stability conditions of the no-delay model as a benchmark. Second, it examines the delay model and analytically establishes the stability switching curve on which stability is switched to instability and vice versa. Finally, numerical simulations are performed to confirm the theoretical results such as Hopf bifurcations and, further, demonstrate a wide variety of dynamics ranging from simple limit cycle to the existence of multi-stability and the birth of chaotic dynamics.

Coexistence and bistability of a competition model with mixed dispersal strategy

In this paper, we investigate a Lotka–Volterra competition model with Danckwerts boundary conditions in a one-dimensional habitat where one species assumes pure random diffusion while another one undergoes mixed movement (both random and directed movements). We focus on the joint influence of advection rate, intrinsic growth rate and interspecific competition coefficient on the competition outcomes. It turns out that there exist some critical curves which separate the stable region of the semitrivial steady states from the unstable one. The locations of these curves determine whether coexistence or bistability occurs. More precisely, there are various tradeoffs between advection rate, intrinsic growth rate and interspecific competition coefficient that allow the transition of competition outcomes including competition exclusion, coexistence and bistability. We illustrate our results in various parameter spaces.

Asymptotic stability of the critical pulled front in a Lotka-Volterra competition model

We prove that the critical pulled front of Lotka-Volterra competition systems is nonlinearly asymptotically stable. More precisely, we show that perturbations of the critical front decay algebraically with rate t−3/2 in a weighted L∞ space. Our proof relies on pointwise semigroup methods and utilizes in a crucial way that the faster decay rate t−3/2 is a consequence of the lack of an embedded zero of the Evans function at the origin for the linearized problem around the critical front.

Discrete Competitive Lotka–Volterra Model with Controllable Phase Volume

The simulation of population dynamics and social processes is of great interest in nonlinear systems. Recently, many scholars have paid attention to the possible applications of population dynamics models, such as the competitive Lotka–Volterra equation, in economic, demographic and social sciences. It was found that these models can describe some complex behavioral phenomena such as marital behavior, the stable marriage problem and other demographic processes, possessing chaotic dynamics under certain conditions. However, the introduction of external factors directly into the continuous system can influence its dynamic properties and requires a reformulation of the whole model. Nowadays most of the simulations are performed on digital computers. Thus, it is possible to use special numerical techniques and discrete effects to introduce additional features to the digital models of continuous systems. In this paper we propose a discrete model with controllable phase-space volume based on the competitive Lotka–Volterra equations. This model is obtained through the application of semi-implicit numerical methods with controllable symmetry to the continuous competitive Lotka–Volterra model. The proposed model provides almost linear control of the phase-space volume and, consequently, the quantitative characteristics of simulated behavior, by shifting the symmetry of the underlying finite-difference scheme. We explicitly show the possibility of introducing almost arbitrary law to control the phase-space volume and entropy of the system. The proposed approach is verified through bifurcation, time domain and phase-space volume analysis. Several possible applications of the developed model to the social and demographic problems’ simulation are discussed. The developed discrete model can be broadly used in modern behavioral, demographic and social studies.

Permanence, Extinction and Periodicity to a Stochastic Competitive Model with Infinite Distributed Delays

In this paper, we study a stochastic Lotka–Volterra competitive model with infinite distributed delays. We obtain sufficient but almost necessary conditions for permanence and extinction of species. Competitive exclusion also takes place in some cases. Besides, criteria are established for the existence and uniqueness of a stationary Markov process. Our results not only cover the traditional Lotka–Volterra competition model without environmental noise, but also reflect the influence of noise to model’s dynamics. Moreover there are some challenges to give the existence of periodic solutions for system with periodic coefficients. Via a stochastic comparison approach, we obtain the existence and uniqueness of periodic solutions in distribution.

The minimal wave speed to the Lotka-Volterra competition model

This paper focuses on selection mechanisms of the minimal speed of traveling waves to the Lotka-Volterra reaction-diffusion model. We first establish general conditions for the linear and nonlinear selection by way of an upper and lower solution method. Then some explicit criteria are derived by subtly constructing formulas of upper and lower solutions. The obtained conditions substantially improve or complement the corresponding results in the known references.

Traveling wavefronts for a Lotka–Volterra competition model with partially nonlocal interactions

The purpose of this work is to investigate the existence and stability of monostable traveling wavefronts for a Lotka–Volterra competition model with partially nonlocal interactions. We first establish an innovative lemma for the existence of positive solutions to a system of linear inequalities. By this lemma, we can construct a pair of sub-super-solutions and derive the existence result by applying the technique of monotone iteration method. It is found that if the ratio of the diffusive rate of the species without nonlocal interactions to that of the other species is not greater than a specific value, then the minimal wave speed of the wavefronts is linearly determined. Moreover, by the spectral analysis of the linearized operators, we show that the traveling wavefronts are essentially unstable in the space of uniformly continuous functions. However, if the initial perturbations of the traveling wavefronts belong to certain exponential weighted spaces, then we prove that the traveling wavefronts with noncritical wave speed are asymptotically stable in the exponential weighted spaces.

Higher temperatures generically favour slower-growing bacterial species in multispecies communities.

Temperature is one of the fundamental environmental variables that determine the composition and function of microbial communities. However, a predictive understanding of how microbial communities respond to changes in temperature is lacking, partly because it is not obvious which aspects of microbial physiology determine whether a species could benefit from a change in the temperature. Here we incorporate how microbial growth rates change with temperature into a modified Lotka-Volterra competition model and predict that higher temperatures should-in general-favour the slower-growing species in a bacterial community. We experimentally confirm this prediction in pairwise cocultures assembled from a diverse set of species and show that these changes to pairwise outcomes with temperature are also predictive of changing outcomes in three-species communities, suggesting that our theory may be applicable to more-complex assemblages. Our results demonstrate that it is possible to predict how bacterial communities will shift with temperature knowing only the growth rates of the community members. These results provide a testable hypothesis for future studies of more-complex natural communities and we hope that this work will help to bridge the gap between ecological theory and the complex dynamics observed in metagenomic surveys.

Free boundary problems with nonlocal and local diffusions I: Global solution

We study a class of free boundary problems of ecological models with nonlocal and local diffusions, which are natural extensions of free boundary problems of reaction diffusion systems in there local diffusions are used to describe the population dispersal, with the free boundary representing the spreading front of the species. We prove that such kind of nonlocal and local diffusion problems has a unique global solution, and then show that a spreading-vanishing dichotomy holds. Moreover, criteria of spreading and vanishing, and long time behavior of solution when spreading happens are established for the classical Lotka-Volterra competition and prey-predator models. Compared with free boundary problems of reaction diffusion systems with local diffusions ([10,24,25]), with nonlocal diffusions ([9]) as well as with nonlocal and local diffusions ([14]) (one equation is Cauchy problem and the other one is free boundary problem), the present paper involves some new difficulties, which should be overcome by use of new techniques. This is part I of a two part series, where we prove the existence, uniqueness, regularity and estimates of global solution. The spreading-vanishing dichotomy, criteria of spreading and vanishing, and long-time behavior of solution when spreading happens will be studied in the separate part II ([17]).

Selection mechanism of the minimal wave speed to the Lotka–Volterra competition model

In this paper, we establish some new criteria for linear or nonlinear selection of the minimal speed of traveling wave solutions to the Lotka–Volterra model. The proofs rely on an upper and lower solution method and constructing subtle upper/lower solutions. The obtained results improve or supplement those in the known references.

Global dynamics of the diffusive Lotka–Volterra competition model with stage structure

The global asymptotic behavior of the classical diffusive Lotka–Volterra competition model with stage structure is studied. A complete classification of the global dynamics is given for the weak competition case. It is shown that under otherwise same conditions, the species with shorter maturation time prevails. The method is also applied to the global dynamics of another competition models with time delays.

Lotka–Volterra Competition Mechanism Embedded in a Decision-Making Method

Decision making is a fundamental capability of living organisms, and has recently been gaining increasing importance in many engineering applications. Here, we consider a simple decision-making principle to identify an optimal choice in multi-armed bandit (MAB) problems, which is fundamental in the context of reinforcement learning. We demonstrate that the identification mechanism of the method is well described by using a competitive ecosystem model, i.e., the competitive Lotka--Volterra (LV) model. Based on the "winner-take-all" mechanism in the competitive LV model, we demonstrate that non-best choices are eliminated and only the best choice survives; the failure of the non-best choices exponentially decreases while repeating the choice trials. Furthermore, we apply a mean-field approximation to the proposed decision-making method and show that the method has an excellent scalability of $O(\log N)$ with respect to the number of choices $N$. These results allow for a new perspective on optimal search capabilities in competitive systems.

On the conjecture for the pushed wavefront to the diffusive Lotka-Volterra competition model.

This paper concerns ecological invasion phenomenon of species based on the diffusive Lotka-Volterra competition model. We investigate the spreading speed (or the minimal wave speed of traveling waves) selection to the model and concentrate on the conjecture raised by Roques et al. (J Math Biol 71(2):465-489, 2015). By using an abstract implicit function theorem in a weighted functional space coupled with a perturbation technique, we not only prove this conjecture, but also show that the fast decay behavior of the first species is necessary and sufficient for the nonlinear speed selection of the whole system. This may lead to further significant results on the answer to the original Hosono's conjecture, a problem that has been outstanding for more than twenty years.

Stability analysis of switched systems for cancer treatment by anti-angiogenesis via minimum dwell time (MDT)

Anti-angiogenic therapy is a novel treatment approach for cancer that aims at preventing a tumor from developing its own blood supply system that it needs for growth. In this paper we consider a mathematical model for cancer with treatment by using Lotka-Volterra Competition model. In order to minimize the side effects for treatment, we propose a switched system to determine the duration of treatments by using the MDT method and provide an analytical insight into the effectiveness of such method. An illustrative example is presented to show the validity of the results.

The dynamics of nonlocal diffusion systems with different free boundaries

<p style='text-indent:20px;'>This paper is concerned with a class of free boundary models with "nonlocal diffusions'' and different free boundaries, which are natural extensions of free boundary problems of reaction diffusion systems with different free boundaries in [M.X.Wang and Y.Zhang, J. Differ. Equ., <b>264</b> (2018), 3527-3558] and references therein. These different free boundaries, which may intersect each other as time evolves, are used to describe the spreading front of the species. We prove that such kind of nonlocal diffusion problems has a unique global solution. Moreover, we investigate the long time behavior of global solution and criteria of spreading and vanishing for the classical Lotka-Volterra competition, prey-predator and mutualist models.

一类时间周期的时滞竞争系统行波解的存在性

A time-periodic reaction-diffusion Lotka-Volterra competition model with delay was considered. Under certain conditions, with the method of super- and sub-solutions and monotone iterations, the existence of time-periodic traveling waves connecting 2 semi-trivial periodic solutions of the corresponding kinetic system was proved with wave speed c<c^*.Furthermore, the traveling wave solutions for c<c^* were proved to be monotone with the comparison principle, and the asymptotic behaviors of traveling wave solutions were obtained at minus/plus infinity. Finally, the existence of traveling wave solutions was proved at wave speed c=c^*.

Bistable wave speed of the Lotka-Volterra competition model

This work deals with the speed sign of travelling waves to the Lotka-Volterra model with diffusion and bistable nonlinearity. We obtain new conditions for the determinacy of the sign of the bistable wave speed by constructing upper or lower solutions with an inside parameter to be adjusted. The established conditions improve or supplement the results in the references and give insight into the combined effect of system parameters on the propagation direction of the bistable wave.