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具有修正的Lelie-Gower项Holling-III类时滞捕食系统的Hopf分支

DOI: 10.3724/SP.J.1004.2013.00610, PP. 610-616

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Abstract:

?研究了一类具有修正的Leslie-Gower项与Holling-III类功能性反应函数的时滞捕食系统.以时滞为分支参数,讨论系统正平衡点的局部稳定性,给出系统产生Hopf分支的时滞关键值.进一步,确定系统Hopf分支的方向与分支周期解稳定性,并对系统全局分支周期解的存在性进行讨论.最后,利用仿真实例验证理论分析结果的正确性.

References

[1]  Zhang S W, Dong L Z, Chen L S. The study of predator-prey system with defensive ability of prey and impulsive perturbations on the predator. Chaos, Solitons and Fractals, 2005, 23(2): 631-643
[2]  Song Y L, Yuan S L, Zhang J M. Bifurcation analysis in the delayed Leslie-Gower predator-prey system. Applied Mathematical Modelling, 2009, 33(11): 4049-4061
[3]  Zhang L, Lin Z G. A H?lling's type II prey-predator model with stage structure and nonlocal delay. Applied Mathematics and Computation, 2011, 217(10): 5000-5010
[4]  Jiang G R, Lu Q S, Qian L N. Complex dynamics of a Holling type II prey-predator system with state feedback control. Chaos, Solitons and Fractals, 2007, 31(2): 448-461
[5]  Nie L F, Teng Z D, Hu L, Peng J G. Qualitative analysis of a modified Leslie-Gower and Holling-type II predator-prey model with state dependent impulsive effects. Nonlinear Analysis: Real World Applications, 2010, 11(3): 1364-1373
[6]  Lv J L, Wang K. Asymptotic properties of a stochastic predator-prey system with Holling II functional response. Communications in Nonlinear Science and Numerical Simulation, 2011, 16(10): 4037-4048
[7]  Cai Z W, Huang L H, Chen H B. Positive periodic solution for a multispecies competition-predator system with Holling III functional response and time delays. Applied Mathematics and Computation, 2011, 217(10): 4866-4878
[8]  Leslie P H. A stochastic model for studying the properties of certain biological systems by numerical methods. Biometrika, 1958, 45(1-2): 16-31
[9]  Gao Z W, Breikin T, Wang H. Reliable observer-based control against sensor failures for systems with time delays in both state and input. IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans, 2008, 38(5): 1018-1029
[10]  Kar T K, Ghorai A. Dynamic behaviour of a delayed predator-prey model with harvesting. Applied Mathematics and Computation, 2011, 217(22): 9085-9104
[11]  Tian Y L, Weng P X. Stability analysis of diffusive predator-prey model with modified Leslie-Gower and Holling-type III schemes. Applied Mathematics and Computation, 2011, 218(7): 3733-3745
[12]  Ruan S G, Wei J J. On the zeros of transcendental functions with applications to stability of delay differential equations with two delays. Dynamics of Continuous, Discrete and Impulsive Systems, 2003, 10(6): 863-874
[13]  Ma Y F. Global Hopf bifurcation in the Leslie-Gower predator-prey model with two delays. Nonlinear Analysis: Real World Applications, 2012, 13(1): 370-375
[14]  Yuan S L, Song Y L. Stability and Hopf bifurcations in a delayed Leslie-Gower predator-prey system. Journal of Mathematical Analysis and Applications, 2009, 355(1): 82-100
[15]  He D C, Huang W T, Xu Q J. The dynamic complexity of an impulsive Holling II predator-prey model with mutual interference. Applied Mathematical Modelling, 2010, 34(9): 2654-2664
[16]  Guo H J, Song X Y. An impulsive predator-prey system with modified Leslie-Gower and Holling type II schemes. Chaos, Solitons and Fractals, 2008, 36(5): 1320-1331
[17]  Etoua R M, Rousseau C. Bifurcation analysis of a generalized Gause model with prey harvesting and a generalized Holling response function of type III. Journal of Differential Equations, 2010, 249(9): 2316-2356
[18]  Lian F Y, Xu Y T. Hopf bifurcation analysis of a predator-prey system with Holling type IV functional response and time delay. Applied Mathematics and Computation, 2009, 215(4): 1484-1495
[19]  Baek H. A food chain system with Holling type IV functional response and impulsive perturbations. Computers and Mathematics with Applications, 2010, 60(5): 1152-1163
[20]  Huang M H, Li X P. Dispersal permanence of a periodic predator-prey system with Holling type-IV functional response. Applied Mathematics and Computation, 2011, 218(2): 502-513
[21]  Holling C S. The functional response of predators to prey density and its role in mimicry and population regulation. Memoirs of the Entomological Society of Canada, 1965, 97(45): 1-60
[22]  Leslie P H. Some further notes on the use of matrices in population mathematics. Biometrika, 1948, 35(3-4): 213-245
[23]  González-Olivares E, Mena-Lorca J, Rojas-Palma A, Flores J D. Dynamical complexities in the Leslie-Gower predator-prey model as consequences of the Allee effect on prey. Applied Mathematical Modelling, 2011, 35(1): 366-381
[24]  Gao Z W, Ding S X. State and disturbance estimator for time-delay systems with application to fault estimation and signal compensation. IEEE Transactions on Signal Processing, 2007, 55(12): 5541-5551
[25]  Nindjin A F, Aziz-Alaoui M A, Cadivel M. Analysis of a predator-prey model with modified Leslie-Gower and Holling-type II schemes with time delay. Nonlinear Analysis: Real World Applications, 2006, 7(5): 1104-1118
[26]  Yafia R, El Adnani F, Alaoui H T. Limit cycle and numerical similations for small and large delays in a predator-prey model with modified Leslie-Gower and Holling-type II schemes. Nonlinear Analysis: Real World Applications, 2008, 9(5): 2055-2067
[27]  Yang Y. Hopf bifurcation in a two-competitor, one-prey system with time delay. Applied Mathematics and Computation, 2009, 214(1): 228-235
[28]  Hassard B D, Kazarinoff N D, Wan Y H. Theory and Applications of Hopf Bifurcation. Cambridge: Cambridge University Press, 1981
[29]  Wu J H. Symmetric functional differential equations and neural networks with memory. Transactions of the American Mathematical Society, 1998, 350(12): 4799-4838

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