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The constants of Lotka–Volterra derivations [PDF]
European Journal of Mathematics, 2015 Let \(R = K[x_{1},\dots, x_{n}]\) be a polynomial ring over a field \(K\) with characteristic zero. Given parameters \(C_{i}\in K\) (\(1\leq i\leq n\)), the Lotka-Volterra (\(K\)-linear) derivation \(d\) of \(R\) is defined on the generators as follows: \(d(x_{i}) = x_{i}(x_{i-1}-C_{i}x_{i+1})\) where the indexing is circular, that is, \(n+e\) and \(e\)
Hegedus, Pál, Zieliński, Janusz
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The field of rational constants of the Volterra derivation; pp. 133–135 [PDF]
Proceedings of the Estonian Academy of Sciences, 2014 We describe the field of rational constants of the four-variable Volterra derivation. Thus, we determine all rational first integrals of its corresponding system of differential equations. Such derivations play a role in population biology, laser physics,
Janusz Zieliński
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Journal of Difference Equations and Applications, 2023 The $q$-Toda equation is derived from replacing ordinary derivatives with $q$-derivatives in the famous Toda equation. In this paper, we associate an extension of the $q$-Toda equation with matrix eigenvalue problems, and then show applications of its time-discretization to computing matrix eigenvalues.
Ryoto Watanabe +2 more
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Jambura Journal of Biomathematics (JJBM), 2021 This paper studies an interaction between one prey and one predator following Lotka-Volterra model with additive Allee effect in predator. The Atangana-Baleanu fractional-order derivative is used for the operator. Since the theoretical ways to investigate the model using this operator are limited, the dynamical behaviors are identified numerically.
Hasan S. Panigoro, Emli Rahmi
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Complexity, 2019 In this paper, a stochastic Lotka–Volterra predator-prey model with discrete delays and feedback control is studied. Firstly, the existence and uniqueness of global positive solution are proved.
Jinlei Liu, Wencai Zhao
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Ecological Modelling, 2015 Abstract Extended logistic and competitive Lotka–Volterra equations were developed by Eizi Kuno to understand the implications of population heterogeneity (especially spatial) for population growth. Population heterogeneity, defined as the presence of individuals in some patches of population and not others, is the resulting expression of a number of
Waters, E K +3 more
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Fractal and Fractional, 2023 This paper studies the dynamic behavior of a class of fractional-order antisymmetric Lotka–Volterra systems. The influences of the order of derivative on the boundedness and stability are characterized by analyzing the first-order and 0<α<1-order antisymmetric Lotka–Volterra systems separately.
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Isotropy group of Lotka-Volterra derivations
Journal of Pure and Applied AlgebraIn this paper, we study the isotropy group of Lotka-Volterra derivations of $K[x_{1},\cdots,x_{n}]$, i.e., a derivation $d$ of the form $d(x_{i})=x_{i}(x_{i-1}-C_{i}x_{i+1})$. If $n=3$ or $n \geq 5$, we have shown that the isotropy group of $d$ is finite. However, for $n=4$, it is observed that the isotropy group of $d$ need not be finite. Indeed, for $
Himanshu Rewri, Surjeet Kour
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The Predator-Prey Model of Tax Evasion: Foundations of a Dynamic Fiscal Ecology
MathematicsTax evasion is a dynamic process reflecting continuous interaction between taxpayers and regulatory institutions rather than a static deviation from fiscal equilibrium.
Miroslav Gombár +2 more
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Discrete & Continuous Dynamical Systems - B, 2008 This well-written paper deals with discrete-time Lotka-Volterra models obtained by applying nonstandard finite difference (NSFD) schemes to the continuous-time counterpart of the model. The NSFD schemes are noncanonical symplectic numerical methods proposed previously by the author [J. Difference Equ. Appl.
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