Influence of strong noise on the decline and propagation of population in the delayed Malthus–Verhulst model

Cai, Jun; Mei, Dong-Cheng

doi:10.1016/j.physa.2010.06.019

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2015

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“…The work of Malthus [10] and Verhulst [13] is the base to the field of the growth and decline of a population [3,16]. In the nature, species do not exist alone.…”

Section: Introductionmentioning

confidence: 99%

Optimal control of a two teams prey-predator interaction model

Aly¹,

Elettreby²

2015

Miskolc Math Notes

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Abstract. In this paper, a model of two teams of predators interacting with two teams of preys is proposed. The predator teams help each other and so do the prey teams. Therefore, some stability analysis are carried out on the model to detect the stability and instability of the system's equilibrium solutions. Also, the persistence of the solutions is investigated. Finally, the optimal control is applied to the unstable equilibrium solutions. Some numerical simulations are carried out to verify the analytic results.2010 Mathematics Subject Classification: 34C23; 35K57; 92D25; 92D30

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“…The work of Malthus [10] and Verhulst [13] is the base to the field of the growth and decline of a population [3,16]. In the nature, species do not exist alone.…”

Section: Introductionmentioning

confidence: 99%

Optimal control of a two teams prey-predator interaction model

Aly¹,

Elettreby²

2015

Miskolc Math Notes

View full text Add to dashboard Cite

show abstract

“…Models of population growth dynamics based on a generalized Verhulst self-regulation mechanism (GVM) [1,2] have found a wide application in studying various fields [3] such as dynamics of biological populations [4,5], autocatalytic chemical reactions [6], laser physics [7], grain growth in polycrystalline materials [8], the spread of viral epidemics [9], tumor cell growth [10], social sciences [11], etc. It should be emphasized that deterministic models, with GVM, of population growth dynamics cannot directly cope with a range of situations dominated by environmental fluctuations in the forcings or in control parameters, which are intrinsic to the phenomenon [12].…”

Section: Introductionmentioning

confidence: 99%