Complex dynamics of a predator–prey system with herd and schooling behavior: with or without delay and diffusion

2021 ◽  
Author(s):  
Jingen Yang ◽  
Sanling Yuan ◽  
Tonghua Zhang
Keyword(s):  
Complex Dynamics ◽  
Predator Prey ◽  
Schooling Behavior ◽  
Prey System ◽  
And Diffusion

scholarly journals Exploring Spatiotemporal Complexity of a Predator-Prey System with Migration and Diffusion by a Three-Chain Coupled Map Lattice

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-19 ◽  
Author(s):  
Tousheng Huang ◽  
Huayong Zhang ◽  
Xuebing Cong ◽  
Ge Pan ◽  
Xiumin Zhang ◽  
...  
Keyword(s):  
Turing Instability ◽  
Coupled Map Lattice ◽  
Self Organization ◽  
Turing Patterns ◽  
Predator Prey ◽  
Migration Rates ◽  
Self Organized ◽  
Prey System ◽  
And Migration ◽  
And Diffusion

The topic of utilizing coupled map lattice to investigate complex spatiotemporal dynamics has attracted a lot of interest. For exploring the spatiotemporal complexity of a predator-prey system with migration and diffusion, a new three-chain coupled map lattice model is developed in this research. Based on Turing instability analysis, pattern formation conditions for the predator-prey system are derived. Via numerical simulation, rich Turing patterns are found with subtle self-organized structures under diffusion-driven and migration-driven mechanisms. With the variation of migration rates, the predator-prey system exhibits a gradual dynamical transition from diffusion-driven patterns to migration-driven patterns. Moreover, new results, the self-organization of non-Turing patterns, are also revealed. We find that even in the cases where the nonspatial predator-prey system reaches collapse, the migration can still drive pattern self-organization. These non-Turing patterns suggest many new possible ways for the coexistence of predator and prey in space, under the effects of migration and diffusion.

scholarly journals Complex Dynamics in a Singular Delayed Bioeconomic Model with and without Stochastic Fluctuation

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Xinyou Meng ◽  
Qingling Zhang
Keyword(s):  
Hopf Bifurcation ◽  
Complex Dynamics ◽  
Hybrid Control ◽  
Positive Equilibrium ◽  
Stochastic Fluctuation ◽  
Predator Prey ◽  
Prey System ◽  
Singularity Induced Bifurcation ◽  
Distribution Of Roots ◽  
Theoretical Results

A singular delayed biological economic predator-prey system with and without stochastic fluctuation is proposed. The conditions of singularity induced bifurcation are gained, and a state feedback controller is designed to eliminate such bifurcation. Furthermore, saddle-node bifurcation is also showed. Next, the local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analyzing the distribution of roots of the corresponding characteristic equation, and the hybrid control strategy is used to control the occurrence of Hopf bifurcation. In addition, some explicit formulas determining the spectral densities of the populations and harvest effort are given when the system is considered with stochastic fluctuation. Finally, numerical simulations are illustrated to verify the theoretical results.

Complex dynamics of a discrete-time predator-prey system with Holling IV functional response

2016 ◽  
Vol 87 ◽  
pp. 158-171 ◽  
Author(s):  
Qianqian Cui ◽  
Qiang Zhang ◽  
Zhipeng Qiu ◽  
Zengyun Hu
Keyword(s):  
Functional Response ◽  
Discrete Time ◽  
Complex Dynamics ◽  
Predator Prey ◽  
Prey System

Predator–Prey System: Bachelor Herding of the Prey Imposes Ecological Constraints on Predation

2021 ◽  
Vol 31 (14) ◽  
Author(s):  
Rajat Kaushik ◽  
Sandip Banerjee
Keyword(s):  
Numerical Simulations ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Herd Behavior ◽  
Ecological Constraints ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Schooling Behavior ◽  
Prey System ◽  
Parent Groups

Bachelor herd behavior is very common among juvenile animals who have not become sexually matured but have left their parent groups. The complex grouping or schooling behavior provides vulnerable juveniles refuge from predation and opportunities for foraging, especially when their parents are not within the area to protect them. In spite of this, juvenile/immature prey may easily become victims because of their greenness while on the other hand, adult prey may be invulnerable to attack due to their tricky manoeuvring abilities to escape from the predators. In this study, we propose a stage-structured predator–prey model, in which predators attack only the bachelor herds of juvenile prey while adult prey save themselves due to small predator–prey size ratio and their fleeing capability, enabling them to avoid confrontation with the predators. Local and global stability analysis on the equilibrium points of the model are performed. Sufficient conditions for uniform permanence and the impermanence are derived. The model exhibits both transcritical as well as Hopf bifurcations and the corresponding numerical simulations are carried out to support the analytical results. Bachelor herding of juvenile prey as well as inaccessibility of adult prey restricts the uncontrolled predation so that prey abundance and predation remain balanced. This investigation on bachelor group defence brings out some unpredictable results, especially close to the zero steady state. Altogether, bachelor herding of the juvenile prey, which causes unconventional behavior near the origin, plays a significant role in establishing uniform permanence conditions, also increases richness of the dynamics in numerical simulations using the bifurcation theory and thereby, shapes ecosystem properties tremendously and may have a large influence on the ecosystem functioning.

Dynamics of a Leslie-Gower predator-prey system with hunting cooperation and prey harvesting

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yong Yao ◽  
Lingling Liu
Keyword(s):  
Complex Dynamics ◽  
Critical Values ◽  
Predator Population ◽  
Predator Prey ◽  
Codimension Two ◽  
Prey System ◽  
Constant Rate ◽  
Risk Of Extinction ◽  
Parameter Values ◽  
Theoretical Results

<p style='text-indent:20px;'>In this paper, we study the dynamics of a Leslie-Gower predator-prey system with hunting cooperation among predator population and constant-rate harvesting for prey population. It is shown that there are a weak focus of multiplicity up to three and a cusp of codimension at most two for various parameter values, and the system exhibits two saddle-node bifurcations, a Bogdanov-Takens bifurcation of codimension two and a Hopf bifurcation as the bifurcation parameters vary. The results developed in this article reveal far more complex dynamics compared to the Leslie-Gower system and show how the prey harvesting and the hunting cooperation affect the dynamics of the system. In particular, there exist some critical values of prey harvesting and hunting cooperation such that the predator and prey populations are at risk of extinction if the intensities of harvesting and hunting cooperation are greater than these critical values. Moreover, numerical simulations are presented to illustrate our theoretical results.</p>

scholarly journals Complex Dynamics on the Routes to Chaos in a Discrete Predator-Prey System with Crowley-Martin Type Functional Response

2018 ◽  
Vol 2018 ◽  
pp. 1-18 ◽  
Author(s):  
Huayong Zhang ◽  
Shengnan Ma ◽  
Tousheng Huang ◽  
Xuebing Cong ◽  
Zichun Gao ◽  
...  
Keyword(s):  
Functional Response ◽  
Complex Dynamics ◽  
Three Dimensional ◽  
Period Doubling ◽  
Flip Bifurcation ◽  
Predator Prey ◽  
Center Manifold Theorem ◽  
Routes To Chaos ◽  
Prey System ◽  
The One

We present in this paper an investigation on a discrete predator-prey system with Crowley-Martin type functional response to know its complex dynamics on the routes to chaos which are induced by bifurcations. Via application of the center manifold theorem and bifurcation theorems, occurrence conditions for flip bifurcation and Neimark-Sacker bifurcation are determined, respectively. Numerical simulations are performed, on the one hand, verifying the theoretical results and, on the other hand, revealing new interesting dynamical behaviors of the discrete predator-prey system, including period-doubling cascades, period-2, period-3, period-4, period-5, period-6, period-7, period-8, period-9, period-11, period-13, period-15, period-16, period-20, period-22, period-24, period-30, and period-34 orbits, invariant cycles, chaotic attractors, sub-flip bifurcation, sub-(inverse) Neimark-Sacker bifurcation, chaotic interior crisis, chaotic band, sudden disappearance of chaotic dynamics and abrupt emergence of chaos, and intermittent periodic behaviors. Moreover, three-dimensional bifurcation diagrams are utilized to study the transition between flip bifurcation and Neimark-Sacker bifurcation, and a critical case between the two bifurcations is found. This critical bifurcation case is a combination of flip bifurcation and Neimark-Sacker bifurcation, showing the nonlinear characteristics of both bifurcations.

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