Related papers: Relationships between the delayed chemostat and th…
We speculate on the role of relativistic versions of delayed differential equations in fundamental physics. Relativistic invariance implies that we must consider both advanced and retarded terms in the equations, so we refer to them as…
A family of non-conjugate chaotic maps generalizing the well-known logistic function is defined, and some of its basic properties studied. A simple formula for the Lyapunov exponents of all the maps contained in this family is given based…
We investigate the solution to the logistic equation involving non-local operators in time. In the linear case such operators lead to the well-known theory of time changes. We provide the probabilistic representation for the non-linear…
In this paper, we discuss the question whether a physical "simplification" of a model makes it always easier to study, at least from a mathematical and numerical point of view. To this end, we give different examples showing that these…
Disordered systems like liquids, gels, glasses, or granular materials are not only ubiquitous in daily life and in industrial applications but they are also crucial for the mechanical stability of cells or the transport of chemical and…
We consider the logistic equation with different types of the piecewise constant argument. It is proved that the equation generates chaos and intermittency. Li-Yorke chaos is obtained as well as the chaos through period-doubling route.…
Delayed processes are ubiquitous throughout biology. These delays may arise through maturation processes or as the result of complex multi-step networks, and mathematical models with distributed delays are increasingly used to capture the…
This study aims to show the fundamental difference between logistic regression and Bayesian classifiers in the case of exponential and unexponential families of distributions, yielding the following findings. First, the logistic regression…
Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…
For the model of periodic chronic myelogenous leukemia considered by Pujo-Menjouet, Mackey et al., model consisting of two delay differential equations, the equation for the density of so-called "resting cells" was studied from numerical…
We study a general chemostat model with a discrete-time delay between consumption and growth. The goal of this article is to provide sufficient and necessary conditions for persistence. This extends previous works in the matter.…
Nowadays the question `what is complexity?' is a challenge to be answered. This question is triggering a great quantity of works in the frontier of physics, biology, mathematics and computer science. Even more when this century has been…
The study of biological cells in terms of mesoscopic, nonequilibrium, nonlinear, stochastic dynamics of open chemical systems provides a paradigm for other complex, self-organizing systems with ultra-fast stochastic fluctuations, short-time…
Dynamical systems with long delay feedback can exhibit complicated temporal phenomena, which once re-organized in a two-dimensional space are reminiscent of spatio-temporal behavior. In this framework, normal forms description have been…
Communication delays and multiplexing are ubiquitous features of real-world networked systems. We here introduce a simple model where these two features are simultaneously present, and report the rich phe- nomenology which is actually due…
Population dynamics and in particular microbial population dynamics, though they are complex but also intrinsically discrete and random, are conventionally represented as deterministic differential equations systems. We propose to revisit…
The article introduces a new relationship between the chemical system complexity and deviation of its bifurcation point from thermodynamic equilibrium. In the formalism of discrete thermodynamics of chemical equilibria, simulation of…
In this article a generalized mathematical model describing the interactions between malignant tumour and immune system with discrete time delay incorporated into the system is considered. Time delay represents the time required to generate…
Stochastic processes with temporal delay play an important role in science and engineering whenever finite speeds of signal transmission and processing occur. However, an exact mathematical analysis of their dynamics and thermodynamics is…
A new q-deformed logistic map is proposed and it is found to have concavity in parts of the x-space. Its one-cycle and two-cycle non-trivial fixed points are obtained which are found to be qualitatively and quantitatively different from…