This paper is concerned with stochastic Lotka–Volterra models perturbed by Lévy noise. Firstly, stochastic logistic models with Lévy noise are investigated. Sufficient and necessary conditions for ...stochastic permanence and extinction are obtained. Then three stochastic Lotka–Volterra models of two interacting species perturbed by Lévy noise (i.e., predator–prey system, competition system and cooperation system) are studied. For each system, sufficient and necessary conditions for persistence in the mean and extinction of each population are established. The results reveal that firstly, both persistence and extinction have close relationships with Lévy noise; Secondly, the interaction rates play very important roles in determining the persistence and extinction of the species.
This paper is concerned with n-species model of facultative mutualism in random environments. The environment variability in this study is characterized with both white noise and color noise modeled ...by Markovian switching. We established new sufficient conditions that ensuring that the system model is positive recurrent. We also showed the existence of a unique ergodic stationary distribution. The presented results are demonstrated by numerical simulations.
The Lotka‐Volterra model is a very famous model and frequently used to describe the dynamics of ecological systems in which two species interact, one a predator and one its prey. In this present ...work, a comparative study is presented for solving Lotka‐Volterra model which has an important role in Biological sciences. The Lotka‐Volterra equations are solved by spectral collocation method (SCM) by using shifted Chebyshev polynomials of first kind. Then, a numerical example with two different cases is presented to demonstrate the accuracy and effectiveness of the numerical schemes. Using spectral method, we get a system of nonlinear algebraic equations which are solved by Newton's iteration method. Also the achieved solutions are compared with another solutions obtained by the Hermite wavelets method (HWM). Further, this work reflects that the integer order Lotka‐Volterra model and the fractional order one have close relationship where integer order model is a special case of fractional order. The behaviors study of predator and prey populations due to presence of fractional derivative are the key features of the present work. Our numerical and graphical results indicate that the proposed methods are simple, powerful and fully compatible for treatment of the Lotka‐Volterra model of fractional order.
Focusing on competitive Lotka–Volterra model in random environments, this paper uses regime-switching diffusions to model the dynamics of the population sizes of
n different species in an ecosystem ...subject to the random changes of the external environment. It is demonstrated that the growth rates of the population sizes of the species are bounded above. Moreover, certain long-run-average limits of the solution are examined from several angles. A partial stochastic principle of competitive exclusion is also derived. Finally, simple examples are used to demonstrate our findings.
We explore the local dynamics, N‐S bifurcation, and hybrid control in a discrete‐time Lotka‐Volterra predator‐prey model in
R+2. It is shown that
∀ parametric values, model has two boundary ...equilibria:
P00(0,0) and
Px0(1,0), and a unique positive equilibrium point:
Pxy+dc,rc−dbc if
c>d. We explored the local dynamics along with different topological classifications about equilibria:
P00(0,0),
Px0(1,0), and
Pxy+dc,rc−dbc of the model. It is proved that model cannot undergo any bifurcation about
P00(0,0) and
Px0(1,0) but it undergoes an N‐S bifurcation when parameters vary in a small neighborhood of
Pxy+dc,rc−dbc by using a center manifold theorem and bifurcation theory and meanwhile, invariant close curves appears. The appearance of these curves implies that there exist a periodic or quasiperiodic oscillations between predator and prey populations. Further, theoretical results are verified numerically. Finally, the hybrid control strategy is applied to control N‐S bifurcation in the discrete‐time model.
Diversified energy power generation is a critical component of China’s West-to-East Electricity Transmission (WEET) project and a key driver of China’s clean energy strategy. Aiming at the complex ...non-linear relationship of inter-regional energy system and fully exploring the information of system data, our paper proposes a novel information-enhanced Grey Lotka–Volterra model (IE-GLVM). The novel model consists of Grey Lotka–Volterra equations and universal network terms, which achieves a clever fusion of energy system competitive relationships and data information-driven modeling in the modeling methodology. In addition, the Joint Gradient Descent method is used to optimally search for all the parameters of the novel model, and we theoretically prove the stability of the algorithm. Based on this, the IE-GLVM model is used to analyze the competitive and cooperative relationships among the three provinces of Sichuan, Hubei, and Jiangsu in the middle line of the WEET project in China under multiple energy sources for power generation and to forecast the future power generation. Eventually, IE-GLVM was compared with three benchmark models, and it demonstrated superior performance in most cases. An analysis and summary of the power generation relationships of each regional energy source were conducted based on the quantitative results of the IE-GLVM model.
•A novel information enhanced grey Lotka–Volterra model is proposed for diversified energy power generation forecasting.•The new model combines the advantages of mechanism modeling with data modeling and improves prediction accuracy.•The model can analyze the competition and cooperation relationship of the electrical structure and predict future.•The joint gradient descent method is proven to smoothly optimize all parameters of the model.•The model is used to analyze the electrical structure in China’s West-to-East Electricity Transmission project.
Stability in distribution, implying the existence of the invariant probability measure, is an important measure of stochastic hybrid system. However, the effect of Lévy jumps on the stability in ...distribution is still unclear. In this paper, we consider a n-species competitive Lotka–Volterra model with Lévy jumps under regime-switching. First, we prove the existence of the global positive solution, obtain the upper and lower boundedness. Then, asymptotic stability in distribution as the main result of our paper is derived under some sufficient conditions. Finally, numerical simulations are carried out to support our theoretical results and a brief discussion is given.
For a stochastic differential equation (SDE) with a unique positive solution, a rational numerical method is expected to be structure preserving. However, most existing methods are not, as far as we ...know. Some characteristics of the SDE models including the multi-dimension and super-linearity make it even more challenging. In this work, we fill the gap by proposing an explicit numerical method which is not only structure preserving but also cost effective. The strong convergence framework is set up by moment convergence analysis. We use the Lotka–Volterra system to elaborate our theory, nevertheless, the method works for a wide range of multi-dimensional superlinear SDE models.
This paper applies the Lotka–Volterra model to investigate the competitive interactions among energy, environment, and economy (3Es) in the U.S. The proposed LV-COMSUD (Lotka–Volterra COmpetition ...Model for SUstainable Development) has satisfactory performance for model fitting and provides a useful multivariate framework to predict outcomes concerning these interactions. Our key findings include a pure competition between emissions and GDP (Gross Domestic Product), neutralisms between renewable and fossil/nuclear energy, and commensalisms between GDP and renewable/fossil energy and between nuclear energy and fossil energy/emissions. These results indicate that renewable/fossil energy use contributes to GDP and interacts indirectly with emissions, that an environmental Kuznets curve exists, and that the amount of produced nuclear energy correlates with emission. The U.S. is dependent on non-clean energy sources and its energy efficiency has room for improvement. The results provide unique insights for policy makers to craft up sustainable economic development plans. Overall, it is suggested that for developed markets such as the U.S., to enhance energy security and mitigate climate changes, improving energy efficiency and developing low-carbon clean energy should be top priorities.
•The competitive interactions among energy, environment, and economy are examined.•A pure competition between emissions and GDP exists and an EKC exists.•Energy use contributes to GDP and interacts indirectly with emissions.•Nuclear energy was used to tackle the growth of emissions/fossil energy use.•Improved energy efficiency is a viable policy to enhance energy security in U.S.
By using the Lotka–Volterra model, this work examines for the first time the feasibility of using low-carbon energy to reduce fossil fuel consumption in the United States and, ultimately, to decrease ...CO2 emissions. The research sample in this work consists of data on energy consumption and CO2 emissions in the United States. Parameter estimation results reveal that although the consumption of low-carbon energy increases the consumption of fossil fuels, the latter does not affect the former. Low-carbon energy usage, including nuclear energy and solar photovoltaic power, increases fossil fuel consumption because the entire lifetime of a nuclear or solar energy facility, from the construction of electricity plants to decommissioning, consumes tremendous amounts of fossil fuels. This result verifies the infeasibility of low-carbon energy to replace fossil fuels under the current mining technology, electricity generation skills and governmental policy in the United States and explains why the United States refused to become a signatory of the Kyoto Protocol. Equilibrium analysis results indicate that the annual consumption of fossil fuels will ultimately exceed that of low-carbon energy by 461%. Since our proposed Lotka–Volterra model accurately predicts the consumption and CO2 emission of different energy sources, this work contributes to the energy policies.
•Our Lotka–Volterra model accurately predicts consumption of different energy sources.•We find the current infeasibility of using low-carbon energy to reduce fossil fuels.•The set-up of nuclear and solar plants increases fossil fuel usage in the U.S.•The consumption of fossil fuels will exceed that of low-carbon energy by 435%.•United States government prefers economic development over environmental protection.
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