Related papers: Relationships between the delayed chemostat and th…
The dynamics of the delay logistic equation with complex parameters and arbitrary complex initial conditions is investigated. The analysis of the local stability of this difference equation has been carried out. We further exhibit several…
A nonautonomous periodic chemostat model with delays modelling $n$ species in competition is considered. Sufficient conditions on the coefficients and consumption functions for the species are given, for both the extinction of the species…
A non-autonomous discrete delayed system for a one-species chemostat based on an Ellermeyer model for the continuous case is studied. Conditions for the persistence or the extinction of the solutions are obtained respectively in terms of…
In this paper, we consider a linear heat equation with constant coefficients and a single constant delay. Such equations are commonly used to model and study various problems arising in ecology and population biology when describing the…
The delayed logistic equation (also known as Hutchinson's equation or Wright's equation) was originally introduced to explain oscillatory phenomena in ecological dynamics. While it motivated the development of a large number of mathematical…
Distributed delay equations have been used to model situations in which there is some sort of delay whose duration is uncertain. However, the interpretation of a distributed delay equation is actually very different from that of a delay…
A proper discretization of the logistic differential equation, which is preserving these two distinct equilibrium solutions and their unstability and stability, suggest that we need to examine the time delay of the logistic map. According…
The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the…
A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…
Logistic equations play a pivotal role in the study of any non linear evolution process exhibiting growth and saturation. The interest for the phenomenology, they rule, goes well beyond physical processes and cover many aspects of ecology,…
We derive an alternative expression for a delayed logistic equation in which the rate of change in the population involves a growth rate that depends on the population density during an earlier time period. In our formulation, the delay in…
A nonlinear cyclic system with delay and the overall negative feedback is considered. The characteristic equation of the linearized system is studied in detail. Sufficient conditions for the oscillation of all solutions and for the…
It is known that few characterization results of the logistic distribution were available before, although it is similar in shape to the normal one whose characteristic properties have been well investigated. Fortunately, in the last…
Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated…
If one isolated species is supposed to evolve following the logistic mapping, then we are tempted to think that the dynamics of two species can be expressed by a coupled system of two discrete logistic equations. As three basic…
In this article, we survey some controversial problems concerning the idea of erasing Which Way information proposed in recent years. A statistical examination of these proposals suggests that whenever the Bayesian rule is taken into…
Logistic functions are good models of biological population growth. They are also popular in marketing in modelling demand-supply curves and in a different context, to chart the sales of new products over time. Delays being inherent in any…
Two symmetrically coupled logistic equations are proposed to mimic the competitive interaction between two species. The phenomena of coexistence, oscillations and chaos are present in this cubic discrete system. This work, together with two…
The main purpose of this paper is to provide a summary of the fundamental methods for analyzing delay differential equations arising in biology and medicine. These methods are employed to illustrate the effects of time delay on the behavior…
Chemistry as an unconventional computing medium presently lacks a systematic approach to gather, store, and sort data over time. To build more complicated systems in chemistries, the ability to look at data in the past would be a valuable…