Ling Bai

Bio: Ling Bai is an academic researcher from Jilin University. The author has contributed to research in topics: Nonlinear system & Population. The author has an hindex of 5, co-authored 8 publications receiving 58 citations. Previous affiliations of Ling Bai include Northeast Normal University.

Optimization problems for general simple population with n-impulsive harvest

Abstract: In this paper, n-impulsive harvest problems of general simple population are discussed by models with Dirac function. The optimal impulsive harvest policies to protect the renewable resource better are obtained under conditions of fixed quantity per impulsive harvest. Then, a concept of the sequence for -optimal harvest moments for general simple population is presented which is beneficial to protect resource better and sustainable development. Finally, we apply the conclusions to some special models.

Gilpin-Ayala model with spatial diffusion and its optimal harvesting policy

Abstract: In this paper we consider spatially nonhomogeneous Gilpin-Ayala diffusive equation suffered from exploitation with spatially variable harvesting effort E(x):@[email protected][email protected]+r(x)u1-(uK(x))^@q-E(x)u,(t,x)@?(0,~)[email protected],u(0,x)[email protected](x),[email protected][email protected],@[email protected]?n=0,[email protected]?(0,~),[email protected][email protected][email protected],which describes the growth of the single-species with Neumann boundary condition and initial value condition. We investigate the global stability of equilibrium solution and optimal harvesting policy. It is found that in the case of ordinary differential equation, our results generalize the spatially homogeneous equations discussed in [C.W. Clark, Mathematical Bio-economics: The Optimal Management of renewable Resources, Wiley, New York, 1976; C.W. Clark, Mathematical Bio-economics: The Optimal Management of Renewable Resources, second ed., Wiley, New York, 1990; M. Fan, K. Wang, Optimal harvesting policy for single population with periodic coefficients, Math. Biosci. 152 (1998) 165; H. Li, A class of single-species models with periodic coefficients and their optimal harvesting policy, J. Biomath. 14(4) (1999) 293], our brief results also generalize the corresponding results in [H. Li, Logistic model for single-species with spatial diffusion and its optimal harvesting policy, J. Biomath. 14(3) (1999) 293] when @q=1.

Analysis of a stochastic ratio-dependent predator–prey model driven by Lévy noise

Abstract: In this paper we consider a non-autonomous ratio-dependent predator–prey system driven by Levy noise. Firstly, we show the existence of global positive solution and stochastic boundedness. Secondly, the conditions of persistent in mean and extinction are established and we also give the asymptotic properties of the solution. Finally, we simulate the model to illustrate our main analytical results.

A diffusive single-species model with periodic coefficients and its optimal harvesting policy

Abstract: In this paper, we consider a Logistic model with spatially nonhomogeneous diffusion under the [email protected][email protected][email protected]=r(x,t)u1-uK(x,t)-E(x,t)u,(x,t)@[email protected](0,~),u(x,0)[email protected](x),[email protected][email protected],@[email protected]?n=0,[email protected]?(0,~),[email protected][email protected][email protected],where coefficients r,K,E are smooth T-periodic functions; this model describes the growth of the single species with the Neumann boundary condition and initial value condition. We investigate the global stability of a periodic solution and optimal harvesting policy. Furthermore, we also consider a generalized single-species model and its harvesting problem. The results gained in this article extend the works in references [Hailong Li, Logistic model for single-species with spatial diffusion and its optimal harvesting policy, J. Biomath., 14 (3) (1999) 293-300 (in Chinese); Ling Bai, Ke Wang, Gilpin-Ayala model with spatial diffusion and its optimal harvesting policy, Appl. Math. Comput., 171 (2005) 531-546].

A diffusive stage-structured model in a polluted environment

Abstract: In this paper we discuss a spatial nonhomogeneous stage-structured self-diffusion model in the polluted environment. The global stability of the equilibrium can be derived based on the stability of the corresponding ordinary differential system using Liapunov function method. The effect of diffusion on the stability of the system is also investigated.

Population dynamical behavior of Lotka-Volterra system under regime switching

Abstract: In this paper, we investigate a Lotka-Volterra system under regime switching dx(t)=diag(x"1(t),,x"n(t))[(b(r(t))+A(r(t))x(t))dt+@s(r(t))dB(t)], where B(t) is a standard Brownian motion The aim here is to find out what happens under regime switching We first obtain the sufficient conditions for the existence of global positive solutions, stochastic permanence and extinction We find out that both stochastic permanence and extinction have close relationships with the stationary probability distribution of the Markov chain The limit of the average in time of the sample path of the solution is then estimated by two constants related to the stationary distribution and the coefficients Finally, the main results are illustrated by several examples

Persistence and extinction of a stochastic single-specie model under regime switching in a polluted environment.

Abstract: This is a continuation of our paper [Liu, M, Wang, K, 2010 Persistence and extinction of a stochastic single-species model under regime switching in a polluted environment, J Theor Biol 264, 934-944] Taking both white noise and colored noise into account, a stochastic single-species model under regime switching in a polluted environment is studied Sufficient conditions for extinction, stochastic nonpersistence in the mean, stochastic weak persistence and stochastic permanence are established The threshold between stochastic weak persistence and extinction is obtained The results show that a different type of noise has a different effect on the survival results

Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps

Abstract: In this paper, we explore an impulsive stochastic infected predator-prey system with Levy jumps and delays. The main aim of this paper is to investigate the effects of time delays and impulse stochastic interference on dynamics of the predator-prey model. First, we prove some properties of the subsystem of the system. Second, in view of comparison theorem and limit superior theory, we obtain the sufficient conditions for the extinction of this system. Furthermore, persistence in mean of the system is also investigated by using the theory of impulsive stochastic differential equations (ISDE) and delay differential equations (DDE). Finally, we carry out some simulations to verify our main results and explain the biological implications.

Bifurcation and optimal harvesting of a diffusive predator–prey system with delays and interval biological parameters ☆

Abstract: This paper deals with a delayed reaction–diffusion three-species Lotka–Volterra model with interval biological parameters and harvesting. Sufficient conditions for the local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analyzing the associated characteristic equation. Furthermore, formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theorem. Then an optimal control problem has been considered. Finally, numerical simulation results are presented to validate the theoretical analysis. Numerical evidence shows that the presence of harvesting can impact the existence of species and over harvesting can result in the extinction of the prey or the predator which is in line with reality.

Dynamics of a stochastic one-prey two-predator model with Lévy jumps

Abstract: Levy noise of one species increases extinction risk of this species and its predator.Levy noise of one species has no impact on the extinction or not of its prey.In some cases, Levy noises do not effect the stability in distribution of the model. This paper is concerned with a one-prey two-predator model with both white noises and Levy noises. We first carry out the almost complete parameters analysis for the model. In each case we show that each species is either persistent in the mean or extinct, depending on some critical values. Then we establish the sufficient criteria for stability in distribution of the model. Finally, we use some numerical examples to demonstrate the analytical findings.