Q -conditional symmetries of the classical diffusive 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 non-Lie ansatz to reduce the diffusive Lotka–Volterra systems with correctly specified coefficients to ODE systems and examples of new exact solutions are found. A possible biological inte...

A wide range of reaction–diffusion systems with constant diffusivities that are invariant under Q-conditional operators is found. Using the symmetries obtained, the reductions of the corresponding systems to the systems of ODEs are conducted in order to find exact solutions. In particular, the solutions of some reaction–diffusion systems of the Lotka–Volterra type in an explicit form and satisf...

We perform an analysis of a recent spatial version of the classical Lotka-Volterra model, where a finite scale controls individuals' interaction. We study the behavior of the predator-prey dynamics in physical spaces higher than one, showing how spatial patterns can emerge for some values of the interaction range and of the diffusion parameter.

We prove that any bounded linear operator on Lp[0, 1] for 1 6 p < ∞, commuting with the Volterra operator V , is not weakly supercyclic, which answers affirmatively a question raised by Léon-Saavedra and Piqueras-Lerena. It is achieved by providing an algebraic flavored condition on an operator which prevents it from being weakly supercyclic and is satisfied for any operator commuting with V . ...

A general charaelerization of multi-input 1'1Ovcmcnt (!clt'ctioH . models is given in terms of tl.e Volterra series formalism. Wheil nonlinearities of order higher than the second arc ncgligibk, an II-input system can be decomposed into a sd of 2-input systems, summing lillearly. For a isymmdrical) 2-inpllt system which h;!s sigllifjcanlnonline:iri~ics only lip 10the second order, (he correlati...

A two-species nonautonomous Lotka-Volterra type model with diffusional migration among the immature predator population, constant delay among the matured predators, and toxicant effect on the immature predators in a nonprotective patch is proposed. The scale of the protective zone among the immature predator population can be regulated through diffusive coefficients Di t , i 1, 2. It is proved ...

Theoretical and empirical studies predict that there should be a decrease in hunting success of predators with increasing prey group size. Most of these studies investigated situations in which predator and prey were in full view of each other before, during and after an attack. In this study, single rock bass Ambloplites rupestris were given an opportunity to launch surprise attacks at shoals ...