FLIP AND N-S BIFURCATION BEHAVIOR OF A PREDATOR-PREY MODEL WITH PIECEWISE CONSTANT ARGUMENTS AND TIME DELAY

doi:10.1016/S0252-9602(17)30102-9

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (6): 1705-1726.doi: 10.1016/S0252-9602(17)30102-9

FLIP AND N-S BIFURCATION BEHAVIOR OF A PREDATOR-PREY MODEL WITH PIECEWISE CONSTANT ARGUMENTS AND TIME DELAY

尚随明^1,2, 田玉¹, 张雅静³

1. School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China;
2. Automation School, Beijing University of Posts and Telecommunications, Beijing 100876, China;
3. School of Science, Agriculture University of Hebei, Baoding 071001, China

收稿日期:2016-07-14 修回日期:2016-10-29 出版日期:2017-12-25 发布日期:2017-12-25
通讯作者: Yu TIAN E-mail:tianyu2992@163.com
作者简介:Suiming SHANG,shangsuiming2015@163.com;Yajing ZHANG,zhangshuxue2000@163.com
基金资助:
This work was supported by Beijing Higher Education Young Elite Teacher (YETP0458).

FLIP AND N-S BIFURCATION BEHAVIOR OF A PREDATOR-PREY MODEL WITH PIECEWISE CONSTANT ARGUMENTS AND TIME DELAY

Suiming SHANG^1,2, Yu TIAN¹, Yajing ZHANG³

1. School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China;
2. Automation School, Beijing University of Posts and Telecommunications, Beijing 100876, China;
3. School of Science, Agriculture University of Hebei, Baoding 071001, China

Received:2016-07-14 Revised:2016-10-29 Online:2017-12-25 Published:2017-12-25
Contact: Yu TIAN E-mail:tianyu2992@163.com
Supported by:
This work was supported by Beijing Higher Education Young Elite Teacher (YETP0458).

摘要/Abstract

摘要：

In this paper, the stability and bifurcation behaviors of a predator-prey model with the piecewise constant arguments and time delay are investigated. Technical approach is fully based on Jury criterion and bifurcation theory. The interesting point is that the model will produce two different branches by limiting branch parameters of different intervals. Besides, image simulation is also given.

关键词: piecewise constant arguments, time delay, flip bifurcation, N-S bifurcation, stability

Abstract:

Key words: piecewise constant arguments, time delay, flip bifurcation, N-S bifurcation, stability

尚随明, 田玉, 张雅静. FLIP AND N-S BIFURCATION BEHAVIOR OF A PREDATOR-PREY MODEL WITH PIECEWISE CONSTANT ARGUMENTS AND TIME DELAY[J]. 数学物理学报(英文版), 2017, 37(6): 1705-1726.

Suiming SHANG, Yu TIAN, Yajing ZHANG. FLIP AND N-S BIFURCATION BEHAVIOR OF A PREDATOR-PREY MODEL WITH PIECEWISE CONSTANT ARGUMENTS AND TIME DELAY[J]. Acta mathematica scientia,Series B, 2017, 37(6): 1705-1726.

参考文献

[1] Lotka A. Elements of Physical Biology. Baltimore:Williams & Wilkins Company, 1925
[2] AlNoufaeya K S, Marchantb T R, Edwardsb M P. The diffusive Lotka-Volterra predator-prey system with delay. Math Biosci, 2015, 270:30-40
[3] Lotka A J. Contribution to the theory of periodic reaction. J Phys Chem, 1910, 14(3):271-274
[4] Goel N S, et al. On the Volterra and Other Non-linear Models of Interacting Populations. Academic Press Inc, 1971
[5] Berryman A A. The origins and evolution of predator-prey theory. Ecology, 1992, 73(5):1530-1535
[6] Rosenzweig M L, MacArthur R H. Graphical representation and stability conditions of predator-prey interactions. Am Nat, 1963:209-223
[7] Jost C, Devulder G, Vucetich J A, Peterson R, Arditi R. The wolves of isle royale display scale-invariant satiation and density dependent predation on moose. J Anim Ecol, 2005, 74(5):809-816
[8] Wang J, Shi J. Perdator-pery system with strong Allee effect in prey. J Math Biology, 2011, 62(3):291-331
[9] Qi J, Su Z Y. Predator-prey system with positive effect for prey. Acta Ecologica Sinica, 2011, 31(24):7474-7478
[10] Kot M. Elements of Mathematical Ecology. London:The Cambridge University Press, 2011:107-160
[11] Maritin A, RUAN S. Predator-prey models with delay and prey harvesting. J Math Biology, 2011, 43(3):247-267
[12] He Z M, Lai X. Bifurcation and chaotic behavior of a discrete-time predator-prey system. Nonlinear Anal RWA, 2011, 12(1):403-417
[13] Khoshsiar G R, Alidoustia J, Bayati E A. Stability and dynamics of a fractional order Leslie-Gower predatorprey model. Appl Math Mode, 2016, 40(3):2075-2086
[14] Tang H, Liu Z H. Hopf bifurcation for a predator-prey model with age structure. Appl Math Mode, 2016, 40(2):726-737
[15] Buffoni G, Groppi M, Soresina C. Dynamics of predator-prey models with a strong Allee effect on the prey and predator-dependent trophic functions. Nonlinear Anal RWA, 2016, 30:143-169
[16] AlNoufaey K S, Marchant T R, Edwards M P. The diffusive Lotka-Volterra predator-prey system with delay. Math Biosci, 2015, 270:30-40
[17] Yang L, Zhang Y M. Positive steady states and dynamics for a diffusive predator-prey system with a degeneracy. Acta Math Sci, 2016, 36B(2):537-548
[18] Yousefnezhad M, Monammadi S A. Stability of a predator-prey system with prey taxis in a general class of functional responses. Acta Math Sci, 2016, 36B(1):62-72
[19] Zeng X Z, Gu Y G. Persistence and the global dynamics of the positive solutions for a ratio-dependent predator-prey system with a crowding term in the prey equation. Acta Math Sci, 2016, 36B(3):689-703
[20] Gupta R D, Kundn D. Generalized exponential distributions:different methods of estimation. J Statist Computs Simu, 2001, 69(3):315-338
[21] Kundn D, Gupta R D. Generalized exponential distributions:Bayesian estimations. Comput Statist Data Analsis, 2008, 52:1873-1883
[22] Chen S Y, Zhang Y. Stability and bifurcation analysis of a predator-prey model with piecewise constant arguments. J Lanzhou university (Natural Science), 2012, 48(3):103-117
[23] Chen S Y, Jin B. Neimark-Sacker bifurcation behavior of predator-prey system with piecewise constant arguments. Acta Ecologica Sinica, 2015, 35(7):2339-2348
[24] Gurcan F, Kartal S, Ozturk I, Bozkurt F. Stability and bifurcation analysis of a mathematical model for tumor-immune interaction with piecewise constant arguments of delay. Chaos Solitons Fractals, 2014, 68:169-179
[25] Zheng B D, Liang L J, Zhang C R. Extended jury criterion. Sci China Math, 2010, 53(4):1133-1150
[26] Yuri A, Kuznetsov. Elements of Applied Bifurcation Theory. New York:Springer-Verlag, Science Press, 1998:106-163
[27] Carr J. Application of the Center Manifold Theory. New York:Springger-Verlag, 1981

FLIP AND N-S BIFURCATION BEHAVIOR OF A PREDATOR-PREY MODEL WITH PIECEWISE CONSTANT ARGUMENTS AND TIME DELAY

FLIP AND N-S BIFURCATION BEHAVIOR OF A PREDATOR-PREY MODEL WITH PIECEWISE CONSTANT ARGUMENTS AND TIME DELAY

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 10

[1]	陈贵强, Matthew RIGBY. STABILITY OF STEADY MULTI-WAVE CONFIGURATIONS FOR THE FULL EULER EQUATIONS OF COMPRESSIBLE FLUID FLOW[J]. 数学物理学报(英文版), 2018, 38(5): 1485-1514.
[2]	周永辉, 杨赟瑞, 刘克盼. STABILITY OF TRAVELING WAVES IN A POPULATION DYNAMIC MODEL WITH DELAY AND QUIESCENT STAGE[J]. 数学物理学报(英文版), 2018, 38(3): 1001-1024.
[3]	唐少君, 张澜. NONLINEAR STABILITY OF VISCOUS SHOCK WAVES FOR ONE-DIMENSIONAL NONISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH A CLASS OF LARGE INITIAL PERTURBATION[J]. 数学物理学报(英文版), 2018, 38(3): 973-1000.
[4]	Janusz BRZDȨK, Krzysztof CIEPLINSKI. ON A FIXED POINT THEOREM IN 2-BANACH SPACES AND SOME OF ITS APPLICATIONS[J]. 数学物理学报(英文版), 2018, 38(2): 377-390.
[5]	A. M. NAGY, N. H. SWEILAM. NUMERICAL SIMULATIONS FOR A VARIABLE ORDER FRACTIONAL CABLE EQUATION[J]. 数学物理学报(英文版), 2018, 38(2): 580-590.
[6]	P. BASKAR, S. PADMANABHAN, M. SYED ALI. FINITE-TIME H_∞ CONTROL FOR A CLASS OF MARKOVIAN JUMPING NEURAL NETWORKS WITH DISTRIBUTED TIME VARYING DELAYS-LMI APPROACH[J]. 数学物理学报(英文版), 2018, 38(2): 561-579.
[7]	Rakesh KUMAR, Anuj Kumar SHARMA, Kulbhushan AGNIHOTRI. STABILITY AND BIFURCATION ANALYSIS OF A DELAYED INNOVATION DIFFUSION MODEL[J]. 数学物理学报(英文版), 2018, 38(2): 709-732.
[8]	杨兆星, 张国宝. GLOBAL STABILITY OF TRAVELING WAVEFRONTS FOR NONLOCAL REACTION-DIFFUSION EQUATIONS WITH TIME DELAY[J]. 数学物理学报(英文版), 2018, 38(1): 289-302.
[9]	Iz-iddine EL-FASSI, Janusz BRZDȨK, Abdellatif CHAHBI, Samir KABBAJ. ON HYPERSTABILITY OF THE BIADDITIVE FUNCTIONAL EQUATION[J]. 数学物理学报(英文版), 2017, 37(6): 1727-1739.
[10]	R. AGARWAL, S. HRISTOVA, P. KOPANOV, D. O'REGAN. IMPULSIVE DIFFERENTIAL EQUATIONS WITH GAMMA DISTRIBUTED MOMENTS OF IMPULSES AND P-MOMENT EXPONENTIAL STABILITY[J]. 数学物理学报(英文版), 2017, 37(4): 985-997.
[11]	郑筱筱, 尚亚东, 彭小明. ORBITAL STABILITY OF PERIODIC TRAVELING WAVE SOLUTIONS TO THE GENERALIZED ZAKHAROV EQUATIONS[J]. 数学物理学报(英文版), 2017, 37(4): 998-1018.
[12]	Alexander ALEKSANDROV, Elena ALEKSANDROVA, Alexey ZHABKO, 陈阳舟. PARTIAL STABILITY ANALYSIS OF SOME CLASSES OF NONLINEAR SYSTEMS[J]. 数学物理学报(英文版), 2017, 37(2): 329-341.
[13]	Mohammed Salah M'HAMDI, Chaouki AOUITI, Abderrahmane TOUATI, Adel M. ALIMI, Vaclav SNASEL. WEIGHTED PSEUDO ALMOST-PERIODIC SOLUTIONS OF SHUNTING INHIBITORY CELLULAR NEURAL NETWORKS WITH MIXED DELAYS[J]. 数学物理学报(英文版), 2016, 36(6): 1662-1682.
[14]	Soumaya SÂANOUNI, Nihed TRABELSI. A BIFURCATION PROBLEM ASSOCIATED TO AN ASYMPTOTICALLY LINEAR FUNCTION[J]. 数学物理学报(英文版), 2016, 36(6): 1731-1746.
[15]	秦晓红, 王腾, 王益. GLOBAL STABILITY OF WAVE PATTERNS FOR COMPRESSIBLE NAVIER-STOKES SYSTEM WITH FREE BOUNDARY[J]. 数学物理学报(英文版), 2016, 36(4): 1192-1214.