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On a Hamiltonian version of a 3D Lotka-Volterra system
Hamiltonian dynamics Lotka-Volterra system stability of equilibria Poincar´ e compactification energy-Casimir mapping
2011/7/7
In this paper we present some relevant dynamical properties of a 3D Lotka-Volterra system from the Poisson dynamics point of view.
Conditional symmetries and exact solutions of the diffusive Lotka-Volterra system
Lotka-Volterra system reaction-diffusion system Lie symmetry
2011/2/28
Q-conditional symmetries of the classical Lotka-Volterra system in the case of one space variable are completely described and a set of such symmetries in explicit form is constructed. The relevant no...
Multistep epsilon-algorithm, Shanks' transformation, and Lotka-Volterra system by Hirota's method
Multistep epsilon-algorithm Shanks' transformation Lotka-Volterra system Hirota's method
2011/2/28
In this paper, we give a multistep extension of the "–algorithm of Wynn, and we show that it implements a multistep extension of the Shanks’ sequence transformation which is cdefined by ratios of dete...
On certain new integrable second order nonlinear differential equations and their connection with two dimensional Lotka-Volterra system
arbitrary parameters integrable cases
2010/4/1
In this paper, we consider a second order nonlinear ordinary differential equation of the form
$\ddot{x}+k_1\frac{\dot{x}^2}{x}+(k_2+k_3x)\dot{x}+k_4x^3+k_5x^2+k_6x=0$, where $k_i$'s, $i=1,2,...,6,$...