Chaos and adaptive control in two prey, one predator system with nonlinear feedback

El-Gohary, Awad; Al-Ruzaiza, A. S.

doi:10.1016/j.chaos.2006.03.101

Cited by 56 publications

(30 citation statements)

References 22 publications

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“…Studies show that changing the values of ω, C1 and C2 in the PSO search process will improve the PSO's performance (El-Gohary et al, 2007;Song et al, 2008;Acharjee et al, 2010;Chuang et al, 2011). In this study, current research progress in improving PSO's performance will be introduced to improve PSO algorithm.…”

Section: Improved Pso Algorithmmentioning

confidence: 95%

Improving flood forecasting capability of physically based distributed hydrological models by parameter optimization

Chen

2016

Hydrol. Earth Syst. Sci.

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Abstract. Physically based distributed hydrological models (hereafter referred to as PBDHMs) divide the terrain of the whole catchment into a number of grid cells at fine resolution and assimilate different terrain data and precipitation to different cells. They are regarded to have the potential to improve the catchment hydrological process simulation and prediction capability. In the early stage, physically based distributed hydrological models are assumed to derive model parameters from the terrain properties directly, so there is no need to calibrate model parameters. However, unfortunately the uncertainties associated with this model derivation are very high, which impacted their application in flood forecasting, so parameter optimization may also be necessary. There are two main purposes for this study: the first is to propose a parameter optimization method for physically based distributed hydrological models in catchment flood forecasting by using particle swarm optimization (PSO) algorithm and to test its competence and to improve its performances; the second is to explore the possibility of improving physically based distributed hydrological model capability in catchment flood forecasting by parameter optimization. In this paper, based on the scalar concept, a general framework for parameter optimization of the PBDHMs for catchment flood forecasting is first proposed that could be used for all PBDHMs. Then, with the Liuxihe model as the study model, which is a physically based distributed hydrological model proposed for catchment flood forecasting, the improved PSO algorithm is developed for the parameter optimization of the Liuxihe model in catchment flood forecasting. The improvements include adoption of the linearly decreasing inertia weight strategy to change the inertia weight and the arccosine function strategy to adjust the acceleration coefficients. This method has been tested in two catchments in southern China with different sizes, and the results show that the improved PSO algorithm could be used for the Liuxihe model parameter optimization effectively and could improve the model capability largely in catchment flood forecasting, thus proving that parameter optimization is necessary to improve the flood forecasting capability of physically based distributed hydrological models. It also has been found that the appropriate particle number and the maximum evolution number of PSO algorithm used for the Liuxihe model catchment flood forecasting are 20 and 30 respectively.

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Section: Improved Pso Algorithmmentioning

confidence: 95%

Improving flood forecasting capability of physically based distributed hydrological models by parameter optimization

Chen

2016

Hydrol. Earth Syst. Sci.

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“…On the other hand, it is well-known that predators are often generalists and multi-prey consumption by such predators affects the densities of all the prey species they feed on [4,27]. Allowing the predator to feed on multiple resources can affect the predictions obtained from simple models, which assume the predator to be a specialist, a fact which has been well recognized in theoretical ecology [8,10,12,16,19,33]. Surprisingly enough, aside from a few exceptions [31], most ecoepidemiological models still 'avoid' exploring these more realistic scenarios involving generalist predators with dynamical prey.…”

Section: Introductionmentioning

confidence: 99%

A Generalist Predator Regulating Spread of a Wildlife Disease: Exploring Two Infection Transmission Scenarios

Sen

Banerjee

Морозов

2015

Math. Model. Nat. Phenom.

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Abstract. Ecoepidemiology is a well-developed branch of theoretical ecology, which explores interplay between the trophic interactions and the disease spread. In most ecoepidemiological models, however, the authors assume the predator to be a specialist, which consumes only a single prey species. In few existing papers, in which the predator was suggested to be a generalist, the alternative food supply was always considered to be constant. This is obviously a simplification of reality, since predators can often choose between a number of different prey. Consumption of these alternative prey can dramatically change their densities and strongly influence the model predictions. In this paper, we try to bridge the gap and explore a generic ecoepidemiological system with a generalist predator, where the densities of all prey are dynamical variables. The model consists of two prey species, one of which is subject to an infectious disease, and a predator, which consumes both prey species. We investigate two main scenarios of infection transmission mode: (i) the disease transmission rate is predator independent and (ii) the transmission rate is a function of predator density. For both scenarios we fulfil an extensive bifurcation analysis. We show that including a second dynamical prey in the system can drastically change the dynamics of the single prey case. In particular, the presence of a second prey impedes disease spread by decreasing the basic reproduction number and can result in a substantial drop of the disease prevalence. We demonstrate that with efficient consumption of the second prey species by the predator, the predator-dependent disease transmission can not destabilize interactions, as in the case with a specialist predator. Interestingly, even if the population of the second prey eventually vanishes and only one prey species finally remains, the system with two prey species may exhibit different properties to those of the single prey system.

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“…Some authors discussed the problem of chaos and stability analysis of some biological models such as cancer and tumor model, genital herpes epidemic, stochastic lattice gas prey-predator model and many other models, see, for example, [15][16][17][18][19]. The problem of optimal control of the unstable equilibrium states of cancer self-remission and tumor system using a feedback control approach is studied by Sarkar and Banerjee and El-Gohary [15,19]. The objective of present work is to study the interaction between growing tumor and the replicating Oncolytic virus with a functional response with saturation effect.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modeling and Analysis of Tumor Therapy with Oncolytic Virus

Agarwal¹,

Bhadauria²

2011

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In this paper, we have proposed and analyzed a nonlinear mathematical model for the study of interaction between tumor cells and oncolytic viruses. The model is analyzed using stability theory of differential equations. Positive equilibrium points of the system are investigated and their stability analysis is carried out. Moreover, the numerical simulation of the proposed model is also performed by using fourth order RungeKutta method which supports the theoretical findings. It is found that both infected and uninfected tumor cells and hence tumor load can be eliminated with time, and complete recovery is possible because of virus therapy, if certain conditions are satisfied. It is further found that the system appears to exhibit periodic limit cycles and chaotic attractors for some ranges of the system parameters.

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Chaos and adaptive control in two prey, one predator system with nonlinear feedback

Cited by 56 publications

References 22 publications

Improving flood forecasting capability of physically based distributed hydrological models by parameter optimization

Improving flood forecasting capability of physically based distributed hydrological models by parameter optimization

A Generalist Predator Regulating Spread of a Wildlife Disease: Exploring Two Infection Transmission Scenarios

Mathematical Modeling and Analysis of Tumor Therapy with Oncolytic Virus

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