FROM purely theoretical considerations Lotka (1920) and Volterra (1926) concluded that a biological system consisting of two interdependent species (predator and prey) will exhibit regular periodic fluctuations in respect to the absolute and relative abundance of each species, even when random fluctuations due to external environmental factors have been eliminated. So far as is known this concl...

Multi-species Lotka-Volterra models exhibit greater instability with an increase in diversity and/or connectance. These model systems, however, lack the likely behavior that a predator will prey more heavily on some species if other prey species decline in relative abundance. We find that stability does not depend on diversity and/or connectance in multi-species Lotka-Volterra models with this ...

For a population with any given number of types, we construct a new multivariate Moran process with frequency-dependent selection and establish, analytically, a correspondence to equilibrium Lotka-Volterra phenomenology. This correspondence, on the one hand, allows us to infer the phenomenology of our Moran process based on much simpler Lokta-Volterra phenomenology, and on the other, allows us ...

In [A. Pulgarin. 2012. Dependence of Lotka’s law parameters on the scientific area. Malaysian Journal of Library and Information Science, 17(1): 41-50], the author finds negative correlations between the average number of papers per author and the Lotka exponent and the Lotka constant as well as positive correlations between the latter two parameters. He also finds lower values for the latter t...

This brief communication analyzes the statistics and methods Lotka used to derive his inverse square law of scientific productivity from the standpoint of modern theory. It finds that he violated the norms of this theory by extremely truncating his data on the right. It also proves that Lotka himself played an important role in establishing the commonly used method of identifying power-law beha...

Synopsis Most of the convergence results appearing so far for delayed Lotka-Volterra-type systems require that undelayed negative feedback dominate both delayed feedback and interspecific interactions. Such a requirement is rarely met in real systems. In this paper we present convergence criteria for systems without instantaneous feedback. Roughly, our results suggest that in a Lotka-Volterra-t...

This paper is a review on some recent works on the Liouville integrability of a large class of Lotka-Volterra systems.

Key words and phrases: Lotka-Volterra model of 3-species, nonexistence of closed orbits, existence of nonconstant analytic rst integral, application of vector analysis, generalized May-Leonard model.

In the case of a critical point being a center, the isochronicity problem (or linearizability problem) is far to be solved in general. A progressive way to find necessary conditions for isochronicity is to compute period constants. In this paper, we establish a new recursive algorithm of calculation of the so-called generalized period constants. Furthermore, we verify the new algorithm by the e...

This paper is concerned with the existence of traveling wave solutions in delayed reaction diffusion systems which at least contain multi-species competition, cooperation and predator-prey models with diffusion and delays. By introducing the mixed quasimonotone condition and the exponentially mixed quasimonotone condition, we reduce the existence of traveling wave solutions to the existence of ...