捕食者具有阶段结构Holling II类功能性反应的捕食模型

Abstract

Abstract: By using a continuation theorem based on Gaines and Mawhin's coincidence degree, the authors study the global exisence of positive periodic solutions of a delayed predator-prey system with Holling II type response and stage structure for predator. A set of easily verifiable sufficient conditions is obtained, which improves some known results. Also, by constructing a suitable Lyapunov function, sufficient conditions which guarantee the global attractivity of the positive periodic solution are obtained.

Key words: Periodic solution, Holling II type functional response, Stage structure, Coincidence degree, Delay

CLC Number:

34K20

Chen Fengde;Chen Xiaoxing ;Zhang Huiying. Positive Periodic Solutions of a Delayed Predator-Prey System with Holling Type II Functional Response[J].Acta mathematica scientia,Series A, 2006, 26(1): 93-103.

Trendmd

[1]	Wang Jun, Wang Tianlu, Wen Yanhua, Zhou Xianfeng. Global Solutions of IVP for N-Dimensional Nonlinear Fractional Differential Equations with Delay [J]. Acta mathematica scientia,Series A, 2018, 38(5): 903-910.
[2]	Lan Guijie, Fu Yingjie, Wei Chunjin, Zhang Shuwen. Stationary Distribution and Periodic Solution for Stochastic Predator-Prey Systems with Holling-Type Ⅲ Functional Response [J]. Acta mathematica scientia,Series A, 2018, 38(5): 984-1000.
[3]	Zheng Lifei, Guo Jie, Wu Meihua, Wang Xiaorui, Wan Aying. The Research on a Class of the Predator-Prey-Mutualist System with Delays [J]. Acta mathematica scientia,Series A, 2018, 38(5): 1001-1013.
[4]	Pan Quyu, Tang Yinghui. Analysis of M/G/1 Repairable Queueing System and Optimal Control Policy with a Replaceable Repair Facility Under Delay Min(N,D)-Policy [J]. Acta Mathematica Scientia, 2018, 38(5): 1014-1031.
[5]	Wang Huiling, Gao Jianfang. Oscillation Analysis of Analytical Solutions for a Kind of Nonlinear Neutral Delay Differential Equations with Several Delays [J]. Acta mathematica scientia,Series A, 2018, 38(4): 740-749.
[6]	Liu Gongwei, Diao Lin. On Convexity for Energy Decay Rates of the Second-Order Evolution Equation with Memory and Time-Varying Delay [J]. Acta mathematica scientia,Series A, 2018, 38(3): 527-542.
[7]	Yao Shaowen, Cheng Zhibo. Positive Periodic Solution for Damped Duffing Equation with Singularity [J]. Acta mathematica scientia,Series A, 2018, 38(3): 543-548.
[8]	Luo Liping, Luo Zhenguo, Deng Yihua. Effect of Impulsive Perturbations on Oscillation of Nonlinear Delay Hyperbolic Distributed Parameter Systems [J]. Acta mathematica scientia,Series A, 2018, 38(2): 313-321.
[9]	Wang Wansheng, Zhong Peng, Zhao Xinyang. Long-Time Stability of Nonlinear Neutral Differential Equations with Variable Delay [J]. Acta mathematica scientia,Series A, 2018, 38(1): 96-109.
[10]	Yang Jiashan, Li Tongxing. Oscillation for a Class of Second-Order Damped Emden-Fowler Dynamic Equations on Time Scales [J]. Acta mathematica scientia,Series A, 2018, 38(1): 134-155.
[11]	Liang Zhiqing, Zeng Xiaping, Zhou Zewen, Pang Guoping, Huang Junhua. Existence of Periodic Solution of Holling-Tanner System with State Feedback Impulsive Control [J]. Acta mathematica scientia,Series A, 2018, 38(1): 174-189.
[12]	Li Zhouhong, Zhang Fengshuo, Cao Jinde, Alsaedi Ahmed, Alsaadi Fuad E. Almost Periodic Solution for a Non-Autonomous Two Species Competitive System with Feedback Controls on Time Scales [J]. Acta mathematica scientia,Series A, 2017, 37(4): 730-750.
[13]	Fu Jinbo, Chen Lansun. Positive Periodic Solution of Multiple Species Comptition System with Ecological Environment and Feedback Controls [J]. Acta mathematica scientia,Series A, 2017, 37(3): 553-561.
[14]	Duan Shuangshuang, Huang Shoujun. Blow up of Periodic Solutions for a Class of Keller-Segel Equations Arising in Biology [J]. Acta mathematica scientia,Series A, 2017, 37(2): 326-341.
[15]	Wang Yunzhu, Gao Jianfang. Oscillation Analysis of Numerical Solutions in the θ-Methods for a Kind of Nonlinear Delay Differential Equation [J]. Acta mathematica scientia,Series A, 2017, 37(2): 342-351.

Positive Periodic Solutions of a Delayed Predator-Prey System with Holling Type II Functional Response

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10