We provide quantitative estimates in total variation distance for positive semigroups, which can be non-conservative and non-homogeneous. The techniques relies on a family of conservative semigroups that describes a typical particle and Doeblin’s type conditions inherited from [11] for coupling the associated process. Our aim is to provide quantitative estimates for linear partial differential ...

In this paper, we present a two-species Vicsek model, that describes alignment interactions of self-propelled particles which can either move or not. The model consists in two populations with distinct Vicsek dynamics [42] that interact only via the passage of the particles from one population to the other. The derivation of a macroscopic description of this model is performed using the methodo...

The structure of population boundaries and the biological dynamics that control the edges of major biogeographic regimes are two fundamental questions in biological oceanography with profound consequences to questions ranging from local variations in the marine ecosystem to features in the optical and acoustic properties of the ocean environment. Facing these problems also provides a unique ave...

A large amount of population models use the concept of a carrying capacity. Simulated populations are bounded by invoking finite resources through a survival probability, commonly referred to as the Verhulst factor. The fact, however, that resources are not easily accounted for in actual biological systems makes the carrying capacity parameter ill-defined. Henceforth, we deem it essential to co...

Populating an ontology with a vast amount of data and ensuring the quality of the integration process by means of human supervision seem to be mutually exclusive goals that nevertheless arise as requirements when building practical applications. In our case, we were confronted with the practical problem of populating the EFGT Net, a large-scale ontology that enables thematic reasoning in differ...

We consider a predator-prey population model with prey gathering together for defense purposes. A transmissible unrecoverable disease affects the prey. We characterize the system behavior, establishing that ultimately either only the susceptible prey survive, or the disease becomes endemic, but the predators are wiped out. Another alternative is that the disease is eradicated, with sound prey a...

Continuous bioreactors are critical unit operations in a wide variety of biotechnological processes. While they can be viewed as chemical reactors, bioreactors offer unique modeling and control challenges due to the complexity of the underlying biochemical reactions and the distributed properties of the cell population. The dynamic behavior of continuous bioreactors can be strongly affected by ...

where ri,Ki,αi ∈ C(R,R+), αi > Ki, i = 1,2, τi,σi ∈ C(R,R+), i = 1,2, ri, Ki, αi, τi, σi(i = 1,2) are functions of period ω > 0. Since the study on periodic solutions of a population model is of great interest in mathematical biology [5] and many authors [1, 7] have argued that the discrete-time models governed by difference equations are more appropriate than the continuous ones when the popul...

We present and analyse in this article a mathematical question with a biological origin, the theoretical treatment of which may have far-reaching implications in the practical treatment of cancers. Starting from biological and clinical observations on cancer cells, tumourbearing laboratory rodents, and patients with cancer, we ask from a theoretical biology viewpoint questions that may be trans...

An ecological population model is presented for the purposes of exploring complex synchronization phenomena in biological systems. The model describes a three level predator–prey– resource system which oscillates with Uniform Phase evolution, yet has Chaotic Abundance levels or Amplitudes (UPCA). We investigate the phase synchronization of two nonidentical diffusively coupled phase coherent mod...