Stability and Hopf bifurcation for a delayed predator–prey model with stage structure for prey and Ivlev-type functional response

Hu, Dongpo; Yun-Yun, LI; Liu, Ming; Bai, Yuzhen

doi:10.1007/s11071-020-05467-z

Cited by 33 publications

(9 citation statements)

References 41 publications

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“…where τ 1 and τ 2 represent the feedback delay of the prey and the second predator, respectively. More recently, both gestation delay and feedback delay have been taken into account by many scholars to make the corresponding prey-predator models be more realistic [33][34][35][36][37]. For example, Chen et al [34] investigated the dynamics of the following stagestructured predator-prey system with two time delays and Monod-Haldane response function:…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a fractional three-species food chain system with mixed functional responses and fear effect

Wang

Alsaedi²,

Huang

2023

Preprint

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In this paper, a novel fractional three-species food chain system with Ivlev-type and ratio-dependent functional responses is proposed. Also the fear effect of the middle predator on the prey is taken into account. First the boundedness of the solutions and the existence of positive equilibrium point are investigated for the non-delayed system, and then the delay-induced Hopf bifurcation is dealt with for the delayed system via feedback control method. Some sufficient Hopf bifurcation conditions are obtained based on Hopf bifurcation theorem and stability theorem for fractional dynamical systems. A simulation example is given to support our theoretical results, and especially the effect of the feedback gains and the level of fear on the stability and bifurcation behavior are discussed by illustrations.

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Section: Introductionmentioning

confidence: 99%

Dynamics of a fractional three-species food chain system with mixed functional responses and fear effect

Wang

Alsaedi²,

Huang

2023

Preprint

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“…For example, several practical systems such as controlling systems, network communication systems, manufacturing processes, population dynamics, rocket motors, nuclear reactors, load balancing instability in parallel calculation, and other various physical phenomena can be described by delayed models [19,22,25]. Recently, the influence of time delay in the predator-prey system with functional response functions are studied by many scholars [16][17][18]. The stability analysis of time delay system has been an active field in the control community since time delay can considerably change the performance and stability of a control system [13].…”

Section: Introductionmentioning

confidence: 99%

Exploring The Influence of Time-Delay On The Dynamics of a Two Prey-One Predator System With Quadratic Self-Interaction

Surosh¹,

Ghaziani²,

Alidousti³

2022

DSA

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This work is devoted to studying the effects of time-delay on the dynamics of a two prey-one predator system with quadratic self-interaction. The essential dynamical structures of the delayed system are analyzed by means of local stability analysis and bifurcation theory.Taking the time lag τ as a free parameter, the necessary conditions for the existence of the Hopf bifurcation around the interior equilibrium of the system has been derived both analytically and numerically. It is observed that a Hopf bifurcation occurs when the bifurcation parameter crosses a certain threshold value and it is found that the dynamics of the system can be effected significantly by the time delay which has both stabilizing and destabilizing impacts depending on the magnitude of the delay. Moreover, we derived the explicit formulas in order to determine the direction of the Hopf bifurcation and examine the nature of the bifurcating periodic solution by using the normal form method and the center manifold theorem. Eventually, some numerical simulations are given to verify the derived theoretical analysis.

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“…On the other hand, time delay has become a factor that cannot be ignored in many biological dynamic systems. A large number of studies have revealed that time delay has an important impact on the dynamic characteristics of biological systems and it is common in predator-prey systems, mainly including mature time delay, capture time delay, and pregnancy time delay [33][34][35]. Local stability of the system means that if the initial state is adjacent to the equilibrium state, the system will not vibrate, and its state trajectory will eventually fall to the equilibrium state.…”

Section: Introductionmentioning

confidence: 99%

“…Based on the discussion above, we introduce the diffusion effect of the population [26][27][28][29] and the pregnancy delay of the predator population [33][34][35] into system (5) to explore its impacts on the dynamic characteristics of the ecological competition system, which can be described by…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal Evolution Characteristics of Time‐Delay Ecological Competition Systems with Food‐Limited and Diffusion

et al. 2022

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In this paper, we put forward a time-delay ecological competition system with food restriction and diffusion terms under Neumann boundary conditions. For the case without delay, the conditions for local asymptotic stability and Turing instability are constructed. For the case with delay, the existence of Hopf bifurcation is demonstrated by analyzing the root distribution of the corresponding characteristic equations. Furthermore, by using the normal form theory and the center manifold reduction of partial functional differential equations, explicit formulas are obtained to determine the direction of bifurcations and the stability of bifurcating periodic solutions. Finally, some simulation examples are provided to substantiate our analysis.

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Stability and Hopf bifurcation for a delayed predator–prey model with stage structure for prey and Ivlev-type functional response

Cited by 33 publications

References 41 publications

Dynamics of a fractional three-species food chain system with mixed functional responses and fear effect

Dynamics of a fractional three-species food chain system with mixed functional responses and fear effect

Exploring The Influence of Time-Delay On The Dynamics of a Two Prey-One Predator System With Quadratic Self-Interaction

Spatiotemporal Evolution Characteristics of Time‐Delay Ecological Competition Systems with Food‐Limited and Diffusion

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