相关论文: Persistence criteria for a chemostat with variable…
Directed cell motion in response to an external chemical gradient occurs in many biological phenomena such as wound healing, angiogenesis, and cancer metastasis. Chemotaxis is often characterized by the accuracy, persistence, and speed of…
Cell colonies of bacteria, tumour cells and fungi, under nutrient limited growth conditions, exhibit complex branched growth patterns. In order to investigate this phenomenon we present a simple hybrid cellular automaton model of cell…
We present significantly advanced studies of the previously introduced physical growth mechanism and unite it with biochemical growth factors. Obtained results allowed formulating the general growth law which governs growth and evolutional…
Let $(X_t)_{t \geq 0}$ be a continuous time Markov process on some metric space $M,$ leaving invariant a closed subset $M_0 \subset M,$ called the {\em extinction set}. We give general conditions ensuring either "Stochastic persistence"…
Response time-delay is an ubiquitous phenomenon in biological systems. Here we use a simple stochastic population model with time-delayed switching-rate conversion to quantitatively study the biological influence of the response time-delay…
We are interested in modeling the Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions, in the specific scales of the biological framework of adaptive dynamics.…
A new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a…
We consider a Nicholson's equation with multiple pairs of time-varying delays and nonlinear terms given by mixed monotone functions. Sufficient conditions for the permanence, local stability and global attractivity of its positive…
Signal duration (e.g. the time scales over which an active signaling intermediate persists) is a key regulator of biological decisions in myriad contexts such as cell growth, proliferation, and developmental lineage commitments.…
In this paper, we obtain sufficient conditions for the permanence of a family of nonautonomous systems of delay differential equations. This family includes structured models from mathematical biology, with either discrete or distributed…
We consider the modeling of the dynamics of the chemostat at its very source. The chemostat is classically represented as a system of ordinary differential equations. Our goal is to establish a stochastic model that is valid at the scale…
The purpose of this paper is to show that it is possible to replace Monod's type model of a chemostat by a constraint based model of bacteria at the genome scale. This new model is an extension of the RBA model of bacteria developed in a…
Quantitative assessment of the growth of biological organisms has produced many mathematical equations. Many efforts have been given on statistical identification of the correct growth model from experimental data. Every growth equation is…
Delay differential equations are used as a model when the effect of past states has to be taken into account. In this work we consider delay models of chemical reaction networks with mass action kinetics. We obtain a sufficient condition…
New checkable criteria for persistence of chemical reaction networks are proposed, which extend and complement those obtained by the authors in previous work. The new results allow the consideration of reaction rates which are time-varying,…
Long-term memory is a feature observed in systems ranging from neural networks to epidemiological models. The memory in such systems is usually modeled by the time delay. Furthermore, the nonlocal operators, such as the "fractional order…
We investigate stability of linear delay differential systems. Stability criteria of the systems are derived based on integrals of the fundamental matrix. They are necessary and sufficient conditions for delay-dependent stability of the…
First, we systemize ealier results the uniform persistence for discrete model $A_{n+1}=A_nF(A_{n-m})$ of population growth, where $F:(0,\infty)\to(0,\infty)$ is continuous and strictly decreasing. Second, we investigation the effect of…
The paper is devoted to the study of stability of equilibrium solutions of a delay differential equation that models leukemia. The equation was previously studied in [5] and [6], where the emphasis is put on the numerical study of periodic…
The modelling of memristive devices is an essential part of the development of novel in-memory computing systems. Models are needed to enable the accurate and efficient simulation of memristor device characteristics, for purposes of testing…