Dynamics and response reshaping of nonlinear predator-prey system undergoing random abrupt disturbances

An actual ecological predator-prey system often undergoes random environmental mutations owing to the impact of natural disasters and man-made destruction, which may destroy the balance between the species. In this paper, the stochastic dynamics of the nonlinear predator-prey system considering random environmental mutations is investigated, and a feedback control strategy is proposed to reshape the response of the predator-prey system against random abrupt environmental mutations. A delayed Markov jump system (MJS) is established to model such a predator-prey system. A novel first integral is constructed which leads to better approximation solutions of the ecosystem. Then, by applying the stochastic averaging method based on this novel first integral, the stochastic response of the predator-prey system is investigated, and an analytical feedback control is designed to reshape the response of the ecosystem from the disturbed state back to the undisturbed one. Numerical simulations finally illustrate the accuracy and effectiveness of the proposed procedure.

[1]  Yongqiang Cheng,et al.  Patient-Specific Coronary Artery 3D Printing Based on Intravascular Optical Coherence Tomography and Coronary Angiography , 2019, Complex..

[2]  Z. Teng,et al.  Extinction in nonautonomous Lotka–Volterra competitive system with pure-delays and feedback controls , 2009 .

[3]  W. Wonham.  Random differential equations in control theory , 1970 .

[4]  Xiaole Yue,et al.  The Estimates of the Mean First Exit Time of a Bistable System Excited by Poisson White Noise , 2017 .

[5]  Yong Xu,et al.  Stochastic Dynamics of a Time-Delayed Ecosystem Driven by Poisson White Noise Excitation , 2018, Entropy.

[6]  Lincong Chen,et al.  Random vibration of SDOF vibro-impact oscillators with restitution factor related to velocity under wide-band noise excitations , 2021 .

[7]  Jinlei Liu,et al.  Dynamic Analysis of Stochastic Lotka-Volterra Predator-Prey Model with Discrete Delays and Feedback Control , 2019, Complex..

[8]  Bernd Krauskopf,et al.  Nonlinear Dynamics of Interacting Populations , 1998 .

[9]  Z. G. Ying,et al.  Asymptotic stability of a class of nonlinear stochastic systems undergoing Markovian jumps , 2016 .

[10]  W. Zhu,et al.  Reshaping of the probability density function of nonlinear stochastic systems against abrupt changes , 2019 .

[11]  Weiqiu Zhu,et al.  Nonlinear Stochastic Dynamics and Control in Hamiltonian Formulation , 2006 .

[12]  Stationary Response of a Class of Nonlinear Stochastic Systems Undergoing Markovian Jumps , 2015 .

[13]  R. May,et al.  Stability and Complexity in Model Ecosystems , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[14]  Yan Li,et al.  Adaptive finite-time tracking control for nonlinear systems with unmodeled dynamics using neural networks , 2018, Advances in Difference Equations.

[15]  Jiang-Lun Wu,et al.  Two-time-scales hyperbolic–parabolic equations driven by Poisson random measures: Existence, uniqueness and averaging principles , 2017 .

[16]  G. Cai,et al.  Stochastic analysis of time-delayed ecosystems. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  Chuanyu Wu,et al.  A novel lever-type vibration isolator with eddy current damping , 2021 .

[18]  Stochastic optimal control of predator–prey ecosystem by using stochastic maximum principle , 2016 .

[19]  W. Q. Zhu,et al.  Control of quasi non-integrable Hamiltonian systems for targeting a specified stationary probability density , 2019, Int. J. Control.

[20]  G. Yin,et al.  Averaging principles for SPDEs driven by fractional Brownian motions with random delays modulated by two-time-scale Markov switching processes , 2017, Stochastics and Dynamics.

[21]  P. Turchin.  Complex Population Dynamics: A Theoretical/Empirical Synthesis , 2013 .

[22]  R. Macarthur,et al.  Graphical Representation and Stability Conditions of Predator-Prey Interactions , 1963, The American Naturalist.

[23]  G. Yin,et al.  On hybrid competitive Lotka–Volterra ecosystems , 2009 .

[24]  Xueyong Wei,et al.  Single-electron detection utilizing coupled nonlinear microresonators , 2020, Microsystems & Nanoengineering.

[25]  Z. Ying,et al.  Asymptotic Stability With Probability One of Random-Time-Delay-Controlled Quasi-Integrable Hamiltonian Systems , 2016 .

[26]  Yanfei Jin,et al.  Stochastic stability and bifurcation in a macroeconomic model , 2007 .

[27]  Y Shastri,et al.  Sustainable ecosystem management using optimal control theory: part 2 (stochastic systems). , 2006, Journal of theoretical biology.

[28]  G. Cai,et al.  Stochastic analysis of the Lotka-Volterra model for ecosystems. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Wan-Tong Li,et al.  Positive periodic solutions of a class of delay differential system with feedback control , 2004, Appl. Math. Comput..