Dynamic analysis of a diffusive eco-epidemiological system with fear effect and prey refuge

被引:1
作者
Ma, Tingting [1 ]
Meng, Xinzhu [1 ]
机构
[1] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China
关键词
Eco-epidemiological system; Fear effect; Bi-stability; Hopf bifurcation; Turing instability; PREDATOR MODEL; BIFURCATION; DEFENSE; DELAY; FOOD;
D O I
10.4310/DPDE.2022.v19.n4.a1
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In the evolutionary development of species, the prey can produce the fear effect in the face of predation behaviors. This fear effect may affect the own reproduction growth of the prey. In order to reduce the risk of predation, the prey has the instinct to protect themselves. At the same time, the population is easy vulnerable by disease in the ecosystem. Driven by these biological facts, we propose an eco-epidemiological system with two-predator-one-prey that considers fear effect and prey refuge. At the same time, we consider the impact of spatial diffusion on the stability of the system. We discuss the conditions for the existence of all equilibrium points with biological meanings in non-spatial system. We also obtain local stability conditions for all equilibrium points. We show that the deterministic system is bistable. Kolmogorov analysis is used to analyze the appearance of limit cycles and chaos in the non-spatial system. We consider k as a bifurcation parameter and study the existence of Hopf bifurcation. In the spacial diffusion system, we deduce the local stability conditions of the diffusion system and obtain the occurrence conditions of Turing instability. Numerical simulations are given to explain the phenomena beyond the scope of analytical methods and better understand the complex predator-prey interactions.
引用
收藏
页码:247 / 271
页数:25
相关论文
共 34 条
[1]   EFFECTS OF FEAR AND ANTI-PREDATOR RESPONSE IN A DISCRETE SYSTEM WITH DELAY [J].
Banerjee, Ritwick ;
Das, Pritha ;
Mukherjee, Debasis .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2022, 27 (07) :3643-3661
[2]   Complexity in a prey-predator model with prey refuge and diffusion [J].
Chakraborty, Bhaskar ;
Bairagi, Nandadulal .
ECOLOGICAL COMPLEXITY, 2019, 37 :11-23
[3]  
COLLINGS JB, 1995, B MATH BIOL, V57, P63, DOI 10.1007/BF02458316
[4]   Application of inequalities technique to dynamics analysis of a stochastic eco-epidemiology model [J].
Feng, Tao ;
Meng, Xinzhu ;
Liu, Lidan ;
Gao, Shujing .
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2016,
[5]   Prey-predator dynamics with prey refuge providing additional food to predator [J].
Ghosh, Joydev ;
Sahoo, Banshidhar ;
Poria, Swarup .
CHAOS SOLITONS & FRACTALS, 2017, 96 :110-119
[6]   A predator-prey model with infected prey [J].
Hethcote, HW ;
Wang, WD ;
Han, LT ;
Zhien, M .
THEORETICAL POPULATION BIOLOGY, 2004, 66 (03) :259-268
[7]  
Holling C. S., 1965, Mem ent Soc Canada Ottawa, Vno. 45, P1
[8]   A COMPARISON OF DETERMINISTIC AND STOCHASTIC PREDATOR-PREY MODELS WITH DISEASE IN THE PREDATOR [J].
Hu, Hongxiao ;
Xu, Liguang ;
Wang, Kai .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2019, 24 (06) :2837-2863
[9]   Qualitative analysis of a predator-prey model with constant-rate prey harvesting incorporating a constant prey refuge [J].
Ji, Lili ;
Wu, Chengqiang .
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (04) :2285-2295
[10]   Effect of predator cannibalism and prey growth on the dynamic behavior for a predator-stage structured population model with diffusion [J].
Jia, Yunfeng ;
Li, Yi ;
Wu, Jianhua .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 449 (02) :1479-1501