Stability Analysis of Harvesting Strategies in a Cellular Automata Based Predator-Prey Model

Chen, Qiuwen; Mao, Jingqiao; Liu, Weifeng

doi:10.1007/11861201_32

Cited by 5 publications

(2 citation statements)

References 14 publications

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“…In [10], a preypredator type fishery model with solely prey harvesting was investigated. Also many papers on prey-predator model with harvesting have been studied in [11][12][13][14][15][16][17][18][19][20][21][22]. In [23] and [24], have explored deterministic chaos vs stochastic oscillation in a prey-predator model and global stability of a three-species food chain model with diffusion, respectively.…”

Section: Introductionmentioning

confidence: 99%

A predator-prey model for the optimal control of fish harvesting through the imposition of a tax

Chatterjee¹,

Pal²

2023

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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This paper is devoted to the study of ecosystem based fisheries management. The model represents the interaction between prey and predator population with Holling II functional response consisting of different carrying capacities and constant intrinsic growth rates. We have considered the continuous harvesting of predator only. It is observed that if the intrinsic growth rate of predator population crosses a certain critical value, the system enters into Hopf bifurcation. Our observations indicate that tax, the management object in fisheries system play huge impacts on this system. The optimal harvesting policy is disposed by imposing a tax per unit of predator biomass. The optimal harvest strategy is determined using Pontryagin's maximum principle, which is subject to state equations and control limitations. The implications of tax are also examined. We have derived different bifurcations and global stability of the system. Finally, numerical simulations are used to back up the analytical results.

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Section: Introductionmentioning

confidence: 99%

A predator-prey model for the optimal control of fish harvesting through the imposition of a tax

Chatterjee¹,

Pal²

2023

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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“…It is well known that as the number of agents in a system increases, this may cause simulations investigating long term dynamics to become intractable [15]. Additionally, there is generally a desire to understand how model outcomes change with respect to varying parameter values [8], which again would necessitate possibly thousands of simulations. As described previously, there is not a universal or agreed upon standard to specify these models and in many cases, the mathematical description of the rules are also not specified [14].…”

Section: Introductionmentioning

confidence: 99%

Global Density Analysis for an Off-Lattice Agent-Based Model

Yereniuk¹,

Olson²

2019

SIAM J. Appl. Math.

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Agent-based (AB) or Cellular Automata (CA) models are rule based and are a relatively simple discrete method that can be used to simulate complex interactions of many agents or cells. The relative ease of implementing the computational model is often counterbalanced by the difficulty of performing rigorous analysis to determine emergent behaviors. In addition, without precise definitions of cell interactions, calculating existence of fixed points and their stability is not tractable from an analytical perspective and can become computationally expensive, involving potentially thousands of simulations.Through developing a precise definition of an off-lattice CA or AB model with a specified interaction neighborhood, we develop a general method to determine a Global Recurrence Rule (GRR). This allows estimates of the state densities in time, which can be easily calculated for a range of parameters in the model. The utility of this framework is tested on an Epidemiological Cellular Automata (E-CA) model where agents or cells correspond to people that are in the susceptible, infected, or recovered states. The interaction neighborhoods of cells are determined in a mathematical formulation that allows the GRR to accurately predict the long term behavior and steady states. The modeling framework outlined will be generally applicable to many areas and can be easily extended.

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Cellular automata based simulation of random versus selective harvesting strategies in predator–prey systems

Chen

Recknagel

2008

Ecological Informatics

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Stability Analysis of Harvesting Strategies in a Cellular Automata Based Predator-Prey Model

Cited by 5 publications

References 14 publications

A predator-prey model for the optimal control of fish harvesting through the imposition of a tax

A predator-prey model for the optimal control of fish harvesting through the imposition of a tax

Global Density Analysis for an Off-Lattice Agent-Based Model

Cellular automata based simulation of random versus selective harvesting strategies in predator–prey systems

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