Historical behavior for a class of Lotka–Volterra systems

Uygun Jamilov; Farrukh Mukhamedov

doi:10.1002/mma.8455

Historical behavior for a class of Lotka–Volterra systems

Uygun Jamilov, Farrukh Mukhamedov

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

It is well-known that discrete-time Kolmogorov systems play important role in studying predator-prey models with interactions. A topic of this paper deals with stochastic discrete-time Kolmogorov systems which are called Lotka–Volterra operators. In the present paper, we provide a new class of LV operators, and establish that each of operator from this class has historical behavior, that is, their time averages diverge.

Original language	English
Pages (from-to)	11380-11389
Number of pages	10
Journal	Mathematical Methods in the Applied Sciences
Volume	45
Issue number	17
DOIs	https://doi.org/10.1002/mma.8455
Publication status	Published - Nov 30 2022

Keywords

Kolmogorov system
Lotka–Volterra operator
historical behavior
non-ergodic

ASJC Scopus subject areas

Mathematics(all)
Engineering(all)

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10.1002/mma.8455

Cite this

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title = "Historical behavior for a class of Lotka–Volterra systems",

abstract = "It is well-known that discrete-time Kolmogorov systems play important role in studying predator-prey models with interactions. A topic of this paper deals with stochastic discrete-time Kolmogorov systems which are called Lotka–Volterra operators. In the present paper, we provide a new class of LV operators, and establish that each of operator from this class has historical behavior, that is, their time averages diverge.",

keywords = "Kolmogorov system, Lotka–Volterra operator, historical behavior, non-ergodic",

author = "Uygun Jamilov and Farrukh Mukhamedov",

note = "Funding Information: The second author thanks to the UAEU UPAR Grant No. G00003447 for support. The authors are greatly indebted to anonymous referees for their constructive comments/suggestions which substantially contributed to improving the quality and presentation of this paper. Publisher Copyright: {\textcopyright} 2022 John Wiley & Sons, Ltd.",

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AU - Mukhamedov, Farrukh

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N2 - It is well-known that discrete-time Kolmogorov systems play important role in studying predator-prey models with interactions. A topic of this paper deals with stochastic discrete-time Kolmogorov systems which are called Lotka–Volterra operators. In the present paper, we provide a new class of LV operators, and establish that each of operator from this class has historical behavior, that is, their time averages diverge.

AB - It is well-known that discrete-time Kolmogorov systems play important role in studying predator-prey models with interactions. A topic of this paper deals with stochastic discrete-time Kolmogorov systems which are called Lotka–Volterra operators. In the present paper, we provide a new class of LV operators, and establish that each of operator from this class has historical behavior, that is, their time averages diverge.

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KW - Lotka–Volterra operator

KW - historical behavior

KW - non-ergodic

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JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

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ER -

Historical behavior for a class of Lotka–Volterra systems

Abstract

Keywords

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