a > 0, is one of the most frequently used, and undoubtedly most successful, models of population dynamics. It is now one of the classical examples of self-organization in many natural and artificial systems [1]. It is virtually impossible to list its all applications — for example, the Web search returns more than 60 000 links to pages and on-line publications containing the key words “logistic...

In this work Peter principle (in the hierarchical structure any competent member tends to rise to his level of incompetence) is consistently interpreted as the discrete form of the well-known logistic (Verhulst or Maltusian) equation of the population dynamics. According to such interpretation anti-Peter principle (in the hierarchical structure any incompetent member tends to rise to his level ...

A great deal of academic research, particularly in the social sciences, makes an implicit assumption that the processes being investigated are largely decomposable, meaning that the effects of individual variables identified in one context are likely to be observed in other contexts as well. Many of the statistical tools employed in analyzing social science data, such as regression and structur...

In this paper, we study the existence of positive solutions of a oneparameter family of logistic equations on R+ or on R. These equations are stationary versions of the Fisher equations and the KPP equations. We also study the blow-up region of a sequence of the solutions when the parameter approaches a critical value and the non-existence of positive solutions beyond the critical value. We use...

Difference equations provide an important framework for analysis of dynamical phenomena in biology, ecology, economics, and so forth. For example, in population dynamics discrete systems adequately describe organisms for which births occur in regular, usually short, breeding seasons. Recently the problem of oscillation and nonoscillation of solutions for nonlinear delay difference equations has...

One commonsense notion about causality is that a slight difference in an antecedent condition should lead to only a minor difference in that condition's effect. In discussing the implications of nonlinear dynamical systems theory, also popularly known as chaos theory, for psychology, Barton (January 1994) introduced the concept of sensitive dependence, which challenges the preceding notion. Acc...

On the basis of dynamical principles we derive the Logistic Equation (LE), widely employed (among multiple applications) in the simulation of population growth, and demonstrate that scaleinvariance and a mean-value constraint are sufficient and necessary conditions for obtaining it. We also generalize the LE to multi-component systems and show that the above dynamical mechanisms underlie large ...

In this work we prove the bivariate uniqueness property of the logistic recursive distributional equation, which arise in the study of the random assignment problem, as discussed by Aldous [4]. Using this and the general framework of Aldous and Bandyopadhyay [2], we then conclude that the associated recursive tree process is endogenous. Thus the logistic variables defined by Aldous [4] for find...

The long time behavior of a logistic-type equation modeling the motion of cells is investigated. The equation we consider takes into account birth and death processes using a simple logistic effect as well as a nonlocal motion of cells using a nonlocal Darcy's law with regular kernel. Using the periodic framework we first investigate the well-posedness of the problem before deriving some inform...

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 interesting characteristics of the solutions of this equation, using computations, which does not arise when we consider the same equation with positive real ...