Positive Periodic Solution of a Stage-Structured Species Model with Holling Type IV Functional Response and Cannibalism for Predator

2010 ◽  
Author(s):  
Ming Zhao
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Positive Periodic Solution ◽  
Type Iv

scholarly journals Investigation on dynamics of an impulsive predator–prey system with generalized Holling type IV functional response and anti-predator behavior

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sekson Sirisubtawee ◽  
Nattawut Khansai ◽  
Akapak Charoenloedmongkhon
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Impulsive Control ◽  
Positive Periodic Solution ◽  
Existence Condition ◽  
Predator Prey ◽  
Type Iv ◽  
Prey System ◽  
Existence And Stability ◽  
Predator Behavior

AbstractIn the present article, we propose and analyze a new mathematical model for a predator–prey system including the following terms: a Monod–Haldane functional response (a generalized Holling type IV), a term describing the anti-predator behavior of prey populations and one for an impulsive control strategy. In particular, we establish the existence condition under which the system has a locally asymptotically stable prey-eradication periodic solution. Violating such a condition, the system turns out to be permanent. Employing bifurcation theory, some conditions, under which the existence and stability of a positive periodic solution of the system occur but its prey-eradication periodic solution becomes unstable, are provided. Furthermore, numerical simulations for the proposed model are given to confirm the obtained theoretical results.

scholarly journals Dynamic Analysis of an Impulsively Controlled Predator-Prey Model with Holling Type IV Functional Response

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Yanzhen Wang ◽  
Min Zhao
Keyword(s):  
Functional Response ◽  
Impulsive Control ◽  
Control Strategies ◽  
Positive Periodic Solution ◽  
Pitchfork Bifurcation ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Type Iv ◽  
Prey Model ◽  
Bifurcation Chaos

The dynamic behavior of a predator-prey model with Holling type IV functional response is investigated with respect to impulsive control strategies. The model is analyzed to obtain the conditions under which the system is locally asymptotically stable and permanent. Existence of a positive periodic solution of the system and the boundedness of the system is also confirmed. Furthermore, numerical analysis is used to discover the influence of impulsive perturbations. The system is found to exhibit rich dynamics such as symmetry-breaking pitchfork bifurcation, chaos, and nonunique dynamics.

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