For permanent and partially permanent, uniformly bounded Lotka-Volterra systems, we apply the Split Lyapunov function technique developed for competitive Lotka-Volterra systems to find new conditions that an interior or boundary fixed point of a Lotka-Volterra system with general species-species interactions is globally asymptotically stable. Unlike previous applications of the Split Lyapunov t...

Hirota’s bilinear technique is applied to some integrable lattice systems related to the Bäcklund transformations of the 2DToda, Lotka-Volterra and relativistic LotkaVolterra lattice systems, which include the modified Lotka-Volterra lattice system, the modified relativistic Lotka-Volterra lattice system, and the generalized BlaszakMarciniak lattice systems. Determinant solutions are constructe...

The discrete Lotka power function describes the number of sources (e.g. authors) with items (e.g. publications). As in econometrics, informetrics theory requires functions of a continuous variable j, replacing the discrete variable n. Now j represents item densities instead of number of items. The continuous Lotka power function describes the density of sources with item density j. The discrete...

The Lotka-Volterra equations are a system of equations proposed to provide a simplified model of twospecies predator-prey population dynamics. In this paper, we investigate the problem of adaptive chaos control and synchronization of a generalized Lotka-Volterra system discovered by Samardzija and Greller (1988). The Samardzija-Greller model is a two-predator, one-prey generalization of the Lot...

3 Example: Differentiating the Lotka-Volterra ODE system 2 3.1 The Lotka-Volterra ODE system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3.2 The derivatives of the Lotka-Volterra ODE system . . . . . . . . . . . . . . . . . . 3 3.3 Integration of the original and augmented Lotka-Volterra ODE system with the Runge-Kutta method . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

One may find out the application‎ ‎of mathematics in the areas of ecology‎, ‎biology‎, ‎environmental‎ ‎sciences etc‎. ‎Mathematics is particulary used in the problem of‎ ‎predator-prey known as lotka-Volterra predator-prey equations.‎ ‎Indeed‎, ‎differential equations is employed very much in many areas‎ ‎of other sciences‎. ‎However‎, ‎most of natural problems involve some‎ ‎unknown functions...

Integrability and linearizability of the Lotka–Volterra systems are studied. We prove sufficient conditions for integrable but not linearizable systems for any rational resonance ratio. We give new sufficient conditions for linearizable Lotka–Volterra systems. Sufficient conditions for integrable Lotka–Volterra systems with 3 : q resonance are given. In the particular cases of 3 : 5 and 3 : 4 r...

We present a qualitative analysis of the Lotka-Volterra differential equation within rectangles that are transverse with respect to the flow. In similar way to existing works on affine systems (and positively invariant rectangles), we consider here nonlinear Lotka-Volterra n-dimensional equation, in rectangles with any kind of tranverse patterns. We give necessary and sufficient conditions for ...

In recent years, non-autonomous delay differential equations have been used in the study of population dynamics, ecology and epidemic. Among those equations, a famous model for population is the Lotka-Volterra competition system. Due to the various seasonal effects present in real life situation, it is reasonable and practical to study the Lotka-Volterra competition system with periodic coeffic...

Since the recent research has shown the importance of biological control in many biological systems appearing in nature, this research paper investigates research in the dynamic and chaotic analysis of the generalized Lotka-Volterra three-species biological system, which was studied by Samardzija and Greller (1988). The generalized Lotka-Voterra biological system consists of two predator and on...