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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.
Convolutions of singular measures and applications to the Zakharov system
Convolution estimates transversal submanifolds L2 bounds
2010/12/8
Uniform L2-estimates for the convolution of singular measures with respect to transversal submanifolds are proved in arbitrary space dimen-sion. The results of Bennett-Bez are used to extend previous ...
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, $i=1,2,...,6,$...
Comment on: "New exact solutions of the (3+1)-dimensional Burgers System" [Phys. Lett. A 373 (2009) 181]
(3+1)-dimensional Burgers System exact solutions
2010/4/6
We demonstrate that all exact solutions of the Riccati equation by Dai andWang [C.-Q. Dai, Y.-Y.Wang, Phys. Lett. A 373 (2009) 181-187] are not new and cannot be new because the general solution of th...
PERIODICITY FOR A COOPERATIVE SYSTEM ON TIME SCALES
time scales cooperative system coincidence degree continuation theorem periodic solutions
2008/11/28
In this paper, by using the method of coincidence degree theory, we explore the existence
of periodic solutions for a cooperative ecological model on time scales.
Existence of Limit Cycles in a Predator-Prey System With a Functional Response of the Form Arctan(ax)
Predator prey system limit cycle unctional response
2008/11/25
We consider a predator prey system with the functional response of the form
µ(x) = arctan(ax); a > 0. The main concern in this paper is the existence of
limit cycles for such system. A necessa...