Bifurcation analysis of an ecological model with nonlinear state–dependent feedback control by Poincaré map defined in phase set

Zhang, Qianqian; Tang, Sanyi

doi:10.1016/j.cnsns.2021.106212

Cited by 21 publications

(2 citation statements)

References 28 publications

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“…The model is also known as the prey-predator system, and its state variables represent the population of prey and predator species (Babaci and Shafiee, 2019), (Li et al, 2018), (Qian et al, 2010). If uncontrolled this system may converge to fixed points while under specific parametrization in may also exhibit bifurcations and chaotic behaviour (Singh and Deolio, 2020), (Zhang and Tang, 2022). Several research works have focused on the problems of stability, boundedness and convergence of the Lotka-Volterra model (El-Gohany and Al-Ruzaiza, 2007), (Chen and Chen, 2019).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear optimal and flatness-based control for the multivariable Lotka-Volterra dynamics

Rigatos,

Wira,

Siano

et al. 2024

Preprint

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The multivariable Lokta-Volterra dynamic model has been widely used to describe interacting and competing populations and has found applications in biology, ecology, agricultural production management and in economics. In this article a nonlinear optimal (H-infinity) control method is developed for the Lotka-Volterra system. First, differential flatness properties are proven for the associated state-space model. Next, the state-space description undergoes approximate linearization with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization process takes place at each sampling instance around a time-varying operating point which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector. For the approximately linearized model of the system a stabilizing H-infinity feedback controller is designed. To compute the controller's gains an algebraic Riccati equation has to be repetitively solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. Finally, the performance of the nonlinear optimal control method is compared against a flatness-based control approach implemented in successive loops.

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Section: Introductionmentioning

confidence: 99%

Nonlinear optimal and flatness-based control for the multivariable Lotka-Volterra dynamics

Rigatos,

Wira,

Siano

et al. 2024

Preprint

View full text Add to dashboard Cite

show abstract

“…Thus, impulsive differential equations (IDEs) provide a natural and effective description in modelling such processes, such as integrated pest management [41][42][43], prey-predator system [44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59], competitive system [60][61][62]. In prey-predator system, the human interventions can be divided into prey-dependent [37,41-43, 47, 48, 51-57], predator-dependent [36,37] and ratio-dependent [63] and prey-predator hybrid-dependent [38,39,64,65]. In natural systems, predators and prey are mixed, so it is impossible to determine the exact number of the two species, but their proportions are usually kept constant.…”

Section: Introductionmentioning

confidence: 99%

Complex dynamics of two prey–predator harvesting models with prey refuge and interval‐valued imprecise parameters

Tian

Hua

Sun

2023

Math Methods in App Sciences

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In view of the phenomena that species in nature are affected by the complexity of the ecosystem, some key biological parameters have certain inaccuracy or uncertainty and part of the prey hides in the shelter from predation. Moreover, different species exhibit different living habits, so it is of certain interest to investigate species‐related imprecise biological parameters. Besides, from the perspective of scientific and reasonable exploitation and utilization of fishery resources, two types of harvesting strategies are introduced into the system. Firstly, the dynamic properties of the system guided by continuous harvesting strategy are analyzed, which demonstrates the impact of refuge rate, imprecision indexes and harvesting efforts on the system dynamics. Meanwhile, the bio‐economic equilibrium is discussed, and the optimal harvesting strategy is obtained. Secondly, the complex dynamics of the system induced by weighted harvesting activity are analyzed. The predator‐extinction periodic solution and coexistent order‐1 periodic solution is discussed according to different weights and thresholds. Finally, the correctness of the obtained results and the feasibility of the harvesting strategy are verified through numerical simulation in MATLAB. The results of this study provide a reference for the scientific and reasonable exploitation and utilization of prey–predator fishery resources in the imprecise parameter environment.

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Study on dynamic behavior of two fishery harvesting models: effects of variable prey refuge and imprecise biological parameters

Hua,

Yuan,

Kaibiao

et al. 2023

J. Appl. Math. Comput.

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Bifurcation analysis of an ecological model with nonlinear state–dependent feedback control by Poincaré map defined in phase set

Cited by 21 publications

References 28 publications

Nonlinear optimal and flatness-based control for the multivariable Lotka-Volterra dynamics

Nonlinear optimal and flatness-based control for the multivariable Lotka-Volterra dynamics

Complex dynamics of two prey–predator harvesting models with prey refuge and interval‐valued imprecise parameters

Study on dynamic behavior of two fishery harvesting models: effects of variable prey refuge and imprecise biological parameters

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