Periodic Solution of a Neutral Delay Leslie Predator-Prey Model and the Effect of Random Perturbation on the Smith Growth Model

Li, Tongtong; Zhao, Wencai

doi:10.1155/2020/8428269

Cited by 5 publications

(2 citation statements)

References 38 publications

(57 reference statements)

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“…In biology, the statedependent feedback control means that the control will be implemented only when the population reaches a given threshold level [16][17][18]. This threshold control strategy is applied to solve many practical biological problems, such as the influence between biological populations [19][20][21], integrated pest management [22][23][24], infectious disease control [25][26][27], fishery harvesting [4,5,[28][29][30], etc. Therefore, it is of great practical significance to establish the corresponding mathematical model to describe and study the state-dependent feedback control strategy.…”

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

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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.

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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

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“…Over the past two decades, many efforts had been made to control chaos, such as stability and chaos synchronization, at unstable fixed points. In recent years, many methods had been put forward to control and synchronize chaos, such as OGY method [26], PC method [27], fuzzy control [28], impulsive control method [29,30], stochastic control [31][32][33], linear feedback control [34], delay feedback approach [35][36][37][38][39][40][41][42][43][44], and multiple delay feedback control (MDFC) [45]. Delayed feedback control (DFC) was first proposed by Pyragas [46] in order to stabilize unstable periodic orbits (UPO).…”

Section: Introductionmentioning

confidence: 99%

Feedback Control of a Chaotic Finance System with Two Delays

Jiang

Zhang

2020

Complexity

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In this research, we use the double-delayed feedback control (DDFC) method in order to control chaos in a finance system. Taking delays as parameters, the dynamic behavior of the system is investigated. Firstly, we study the local stability of equilibrium and the existence of local Hopf bifurcations. It can find that the delays can make chaos disappear and generate a stable equilibrium or periodic solution, which means the effectiveness of DDFC method. By using the normal form theory and center manifold argument, one derives the explicit algorithm for determining the properties of bifurcation. In addition, we also apply some mathematical methods (stability crossing curves) to show the stability changes of the financial system in two parameters’ τ1,τ2 plane. Finally, we give some numerical simulations by Matlab Microsoft to show the validity of theoretical analyses.

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A state-dependent impulsive system with ratio-dependent action threshold for investigating SIR model

Li,

Huang,

Xiang

2024

MATH

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<abstract><p>In general, there is an imperative to amalgamate timely interventions and comprehensive measures for the efficacious control of infectious diseases. The deployment of such measures is intricately tied to the system's state and its transmission rate, presenting formidable challenges for stability and bifurcation analyses. In our pursuit of devising qualitative techniques for infectious disease analysis, we introduced a model that incorporates state-dependent transmission interventions. Through the introduction of state-dependent control, characterized by a non-linear action threshold contingent upon the combination of susceptible population density and its rate of change, we employ analytical methods to scrutinize various facets of the model. This encompasses addressing the existence, stability, and bifurcation phenomena concerning disease-free periodic solutions (DFPS). The analysis of the established Poincaré map leads us to the conclusion that DFPS indeed exists and maintains stability under specific conditions. Significantly, we have formulated a distinctive single-parameter family of discrete mappings, leveraging the bifurcation theorems of discrete maps to dissect the transcritical bifurcations around DFPS with respect to parameters such as $ ET $ and $ \eta_{1} $. Under particular conditions, these phenomena may give rise to effects like backward bifurcation and bistability. Through the analytical methodologies developed in this study, our objective is to unveil a more comprehensive understanding of infectious disease models and their potential relevance across diverse domains.</p></abstract>

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Periodic Solution of a Neutral Delay Leslie Predator-Prey Model and the Effect of Random Perturbation on the Smith Growth Model

Cited by 5 publications

References 38 publications

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

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

Feedback Control of a Chaotic Finance System with Two Delays

A state-dependent impulsive system with ratio-dependent action threshold for investigating SIR model

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