An equation of the distributed Volterra-Lotka type, with free boundary of the obstacle type, with possible applications in ecology, when extinction of the biological species is of particular concern, is introduced and solved. Optimal control problem for such an equation, and in particular the problem of minimization of the area of extinction of the species, is introduced and to some extent solved.

In the present paper we study a tri-trophic Lotka-Volterra food web model with omnivory and predator switching. We observe that if the intensity of predator switching increases the chaotic behavior of the omnivory model will be reduced. We conclude that the predator switching mechanism enhances the stability of an otherwise chaotic system.

The molecule solution of an extended discrete Lotka-Volterra equation is constructed, from which a new sequence transformation is proposed. A convergence acceleration algorithm for implementing this sequence transformation is found. It is proved that our new sequence transformation accelerates some kinds of linear sequences and factorial sequences with good numerical stability. Some numerical e...

The purpose of this paper is to investigate several context-free grammars suggested by the Lotka-Volterra system. Some combinatorial arrays, involving the Stirling numbers of the second kind and Eulerian numbers, are generated by these context-free grammars. In particular, we present grammatical characterization of some statistics on cyclically ordered partitions.

Defeat and success of the competitive invasion of a populated area is described with a standard Lotka-Volterra competition model. The resident is adapted to the heterogeneous living conditions, i.e., its motion is modelled as space-dependent, so-called Fokker-Planck diffusion. The invader’s diffusion is taken as neutral Fickian. Furthermore, it is studied how multiplicative environmental noise ...

In 1 , the general nonautonomous n-species Lotka-Volterra competitive systems with impulsive effects are investigated. By using the methods of inequalities estimate and constructing the suitable Liapunov functions, the sufficient conditions on the permanence of whole species and global attractivity of systems are established. In 2 , the authors studied the following general nonautonomous n-spec...

Some techniques of bilinearization of the non-autonomous 1+1 dimensional discrete soliton equations are discussed by taking the discrete KdV equation, the discrete Toda lattice equation, and the discrete Lotka-Volterra equation as examples. Casorati determinant solutions to those equations are also constructed explicitly. §

Systems of linear diierential equations with constant coeecients, as well as Lotka{Volterra equations, with delays in the oo{diagonal terms are considered. Such systems are shown to be asymptotically stable for any choice of delays if and only if the matrix has a negative weakly dominant diagonal.

Fractional differential equations started to have important applications in various fields of science and engineering involving dynamics of complex phenomena. Finding new methods to solve the fractional differential equations is an open issue in the area of fractional calculus. In this paper the homotopy perturbation method is used to find an analytic approximate solution for the coupled Lotka-...

For autonomous Lotka-Volterra systems of differential equations modelling the dynamics of n competing species, new criteria are established for the existence of a single point global attractor. Under the conditions of these criteria, some of the species will survive and stabilise at a steady state whereas the others, if any, will die out.