Dynamic Analysis of Beddington–DeAngelis Predator‐Prey System with Nonlinear Impulse Feedback Control

Li, Dezhao; Cheng, Huidong; Liu, Yu

doi:10.1155/2019/5308014

Cited by 8 publications

(8 citation statements)

References 49 publications

(65 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Many studies devote to the properties of periodic solutions [17][18][19][20], including the existence, stability and periodicity, etc. It has been confirmed that the Poincaré map is a very useful tool to prove the existence of periodic solution in state-dependent impulsive differential equations [21][22][23]. In addition, Simeonov and Bainov [24] gave analogue of Poincaré criterion in ref.…”

Section: Introductionmentioning

confidence: 90%

Dynamic Complexity in a Prey-Predator Model with State-Dependent Impulsive Control Strategy

Dai

2020

Complexity

View full text Add to dashboard Cite

In this paper, an ecological model described by a couple of state-dependent impulsive equations is studied analytically and numerically. The theoretical analysis suggests that there exists a semitrivial periodic solution under some conditions and it is globally orbitally asymptotically stable. Furthermore, using the successor function, we study the existence, uniqueness, and stability of order-1 periodic solution, and the boundedness of solution is also presented. The relationship between order-k successor function and order-k periodic solution is discussed as well, thereby giving the existence condition of an order-3 periodic solution. In addition, a series of numerical simulations are carried out, which not only support the theoretical results but also show the complex dynamics in the model further, for example, the coexistence of multiple periodic solutions, chaos, and period-doubling bifurcation.

show abstract

Section: Introductionmentioning

confidence: 90%

Dynamic Complexity in a Prey-Predator Model with State-Dependent Impulsive Control Strategy

Dai

2020

Complexity

View full text Add to dashboard Cite

show abstract

“…For a herbivore-plankton model with cannibalism, the existence and stability of order-1 periodic solution were discussed in [9], where the model was a system of Impulsive Differential Equations (IDEs), which has more complex and abundant dynamics, but can fully take into account the impact of instantaneous mutations on the state and more deeply reflect the law of things changing. IDEs are widely used in biology, medicine, control theory and other fields [10][11][12][13]. In biology, the impulsive differential equation can be proposed to incorporate the possible changes in the population into the research model, more information can be found from [14,15].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of a Plankton-Herbivore State-Dependent Impulsive Model With Action Threshold Depending On The Density and Its Changing Rate

Zhang

Wang

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

A plankton-herbivore state-dependent impulsive model with nonlinear impulsive functions and action threshold including population density and rate of change is proposed. Since the use of action threshold makes the model have complex phase set and pulse set, we adopt the Poincaré map as a tool to study its complex dynamics. The Poincaré map is defined on the phase set and its properties in different situations are analyzed. Furthermore, the periodic solution of model are discussed, including the existence and stability conditions of the order-1 periodic solution and the existence of the order-k (k ≥ 2) periodic solutions. Compared with the fixed threshold in the existing literature, our results show that the use of action threshold is more practical, which is conducive to the sustainable development of population and makes people obtain more economic benefits. The analysis method used in this paper can study the complex dynamics of the model more comprehensively and deeply.

show abstract

“…Recently, threshold state pulsed dynamic systems have been widely used [7][8][9][10][11][12][13][14]. e geometric theory of impulse dynamical system has been well-developed [15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Complexity of a Phytoplankton-Fish Model with the Impulsive Feedback Control by means of Poincaré Map

Liu

Cheng

2020

Complexity

Self Cite

View full text Add to dashboard Cite

The phytoplankton-fish model for catching fish with impulsive feedback control is established in this paper. Firstly, the Poincaré map for the phytoplankton-fish model is defined, and the properties of monotonicity, continuity, differentiability, and fixed point of Poincaré map are analyzed. In particular, the continuous and discontinuous properties of Poincaré map under different conditions are discussed. Secondly, we conduct the analysis of the necessary and sufficient conditions for the existence, uniqueness, and global stability of the order-1 periodic solution of the phytoplankton-fish model and obtain the sufficient conditions for the existence of the order-kk≥2 periodic solution of the system. Numerical simulation shows the correctness of our results which show that phytoplankton and fish with the impulsive feedback control can live stably under certain conditions, and the results have certain reference value for the dynamic change of phytoplankton in aquatic ecosystems.

show abstract

Dynamic Analysis of Beddington–DeAngelis Predator‐Prey System with Nonlinear Impulse Feedback Control

Cited by 8 publications

References 49 publications

Dynamic Complexity in a Prey-Predator Model with State-Dependent Impulsive Control Strategy

Dynamic Complexity in a Prey-Predator Model with State-Dependent Impulsive Control Strategy

Dynamic Analysis of a Plankton-Herbivore State-Dependent Impulsive Model With Action Threshold Depending On The Density and Its Changing Rate

Dynamic Complexity of a Phytoplankton-Fish Model with the Impulsive Feedback Control by means of Poincaré Map

Contact Info

Product

Resources

About