Switching from simple to complex dynamics in a predator–prey–parasite model: An interplay between infection rate and incubation delay

2016 ◽  
Vol 277 ◽  
pp. 1-14 ◽  
Author(s):  
N. Bairagi ◽  
D. Adak
Keyword(s):  
Infection Rate ◽  
Complex Dynamics ◽  
Predator Prey

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

scholarly journals Predator-prey interactions under fear effect and multiple foraging strategies

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Susmita Halder ◽  
Joydeb Bhattacharyya ◽  
Samares Pal
Keyword(s):  
Complex Dynamics ◽  
Model Simulation ◽  
Prey Population ◽  
Foraging Strategies ◽  
Generalist Predator ◽  
Hopf Bifurcations ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fear Effect ◽  
Simulation Results

<p style='text-indent:20px;'>We propose and analyze the effects of a generalist predator-driven fear effect on a prey population by considering a modified Leslie-Gower predator-prey model. We assume that the prey population suffers from reduced fecundity due to the fear of predators. We investigate the predator-prey dynamics by incorporating linear, Holling type Ⅱ and Holling type Ⅲ foraging strategies of the generalist predator. As a control strategy, we have considered density-dependent harvesting of the organisms in the system. We show that the systems with linear and Holling type Ⅲ foraging exhibit transcritical bifurcation, whereas the system with Holling type Ⅱ foraging has a much more complex dynamics with transcritical, saddle-node, and Hopf bifurcations. It is observed that the prey population in the system with Holling type Ⅲ foraging of the predator gets severely affected by the predation-driven fear effect in comparison with the same with linear and Holling type Ⅱ foraging rates of the predator. Our model simulation results show that an increase in the harvesting rate of the predator is a viable strategy in recovering the prey population.</p>

scholarly journals How Should Cancer Models Be Constructed?

2020 ◽  
Vol 27 (1) ◽  
pp. 107327482096200
Author(s):  
Robert A. Beckman ◽  
Irina Kareva ◽  
Frederick R. Adler
Keyword(s):  
Complex Dynamics ◽  
Full Range ◽  
Evolutionary Game ◽  
Treatment Strategies ◽  
Predator Prey ◽  
Cancer Models ◽  
The Face ◽  
Predator Prey Models ◽  
The Right ◽  
Parameter Values

Choosing and optimizing treatment strategies for cancer requires capturing its complex dynamics sufficiently well for understanding but without being overwhelmed. Mathematical models are essential to achieve this understanding, and we discuss the challenge of choosing the right level of complexity to address the full range of tumor complexity from growth, the generation of tumor heterogeneity, and interactions within tumors and with treatments and the tumor microenvironment. We discuss the differences between conceptual and descriptive models, and compare the use of predator-prey models, evolutionary game theory, and dynamic precision medicine approaches in the face of uncertainty about mechanisms and parameter values. Although there is of course no one-size-fits-all approach, we conclude that broad and flexible thinking about cancer, based on combined modeling approaches, will play a key role in finding creative and improved treatments.

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.

scholarly journals Complex Dynamics of Beddington–DeAngelis-Type Predator-Prey Model with Nonlinear Impulsive Control

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Changtong Li ◽  
Xiaozhou Feng ◽  
Yuzhen Wang ◽  
Xiaomin Wang
Keyword(s):  
Periodic Solution ◽  
Pest Management ◽  
Pest Control ◽  
Natural Enemy ◽  
Complex Dynamics ◽  
Impulsive Control ◽  
Control Strategies ◽  
Resource Limitation ◽  
Predator Prey ◽  
Predator Prey Model

According to resource limitation, a more realistic pest management is that the impulsive control actions should be adjusted according to the densities of both pest and natural enemy in the field, which result in nonlinear impulsive control. Therefore, we have proposed a Beddington–DeAngelis interference predator-prey model concerning integrated pest management with both density-dependent pest and natural enemy population. We find that the pest-eradication periodic solution is globally stable if the impulsive period is less than the critical value by Floquet theorem. The condition of permanent is established, and a stable positive periodic solution appears via a supercritical bifurcation by bifurcation theorem. Finally, in order to investigate the effects of those nonlinear control strategies on the successful pest control, the bifurcation diagrams showed that the model exists with very complex dynamics. Consequently, the resource limitation may result in pest outbreak in complex ways, which means that the pest control strategies should be carefully designed.

Sign in / Sign up

Export Citation Format

Share Document