This paper is devoted to the study of a one-dimensional optimal control problem of Lagrange type under periodic constraints. The system is governed by a Kolmogorov equation including a control term. We show that the set of initial conditions for which there exists a control such that the associated trajectory is periodic is an interval. Thanks to Pontryagin Maximum Principle, we characterize op...

Movement behavior of biological entities plays a crucial role in their destiny through regulating their intraspecific and interspecific interactions as well as their interaction with surrounding environment. In spite of various models for population dynamics, the effect of movement behavior and heterogeneity of environment on population dynamics has remained poorly understood. We introduced an ...

Several predator species at risk of extinction in Southwestern Europe are dependent on the population density of European wild rabbits Oryctolagus cuniculus. Rabbit populations in the region, however, have recently undergone dramatic decreases in population density, which may be exacerbated by hunting. Current hunting policies set the autumn–winter season, just before the start of rabbit reprod...

copepods are the main zooplankton assemblages in most tropical and semi-tropical estuaries. in this research, copepod population dynamics were investigated in helleh river estuary, persian gulf during four seasons beginning from summer 2011 to spring 2012.  samples were taken using plankton net with mesh size of 140 µm and vertical towing from 5 fixed-stations in mid-season. results showed that...

In this exposition we prove an existence theorem for a quantum mechanical dynamical entropy based on von-Neumann’s measurement theory. To that end we introduced a Shannon type of information associated with a quantum channel or measurement based on Araki’s relative entropy. This is an invariance for the dynamics which generalizes Kolmogorov-Sinai ’s notion of dynamical entropy of a measure pres...

In this paper, a Kolmogorov-type model, which includes the Gause-type model (Kuang and Freedman, 1988), the general predator-prey model (Huang 1988, Huang and Merrill 1989), and many other specialized models, is studied. The stability of equilibrium points, the existence and uniqueness of limit cycles in the model are proved.

Despite considerable speculation virtually nothing is known about the empirical relationship between traditional Tibetan administrative systems, household processes, and demographic trends in historical Tibetan populations because indigenous data sources have never been systematically analyzed. This article examines a 1958 tax register from Kyirong, formerly a district-level political division ...

We study the null controllability of Kolmogorov-type equations ∂t f + v ∂x f − ∂2 v f = u(t, x, v)1ω(x, v) in a rectangle , under an additive control supported in an open subset ω of . For γ = 1, with periodic-type boundary conditions, we prove that null controllability holds in any positive time, with any control support ω. This improves the previous result by Beauchard and Zuazua (Ann Ins H P...