We consider a Dirichlet problem for nonlinear, nonlocal equation driven by the degenerate fractional p-Laplacian, with logistic-type reaction depending on positive parameter. In subdiffusive and equidiffusive cases, we prove existence uniqueness of solution when parameter lies in convenient intervals. superdiffusive case, establish bifurcation result. A new strong comparison result, independent...

In his paper on chaos and cryptography, Baptista says ”It is possible to encrypt a message (a text composed by some alphabet) using the ergodic property of the simple low-dimensional and chaotic logistic equation. The basic idea is to encrypt each character of the message as the integer number of iterations performed in the logistic equation, in order to transfer the trajectory from an initial ...

The population growth, is increase in the number of individuals in population and it depends on some random environment effects. There are several different mathematical models for population growth. These models are suitable tool to predict future population growth. One of these models is logistic model. In this paper, by using Feynman-Kac formula, the Adomian decomposition method is applied to ...

After reviewing a number of results from geometric singular perturbation theory, we give an example of a theorem for periodic solutions in a slow manifold. This is illustrated by examples involving the van der Pol-equation and a modified logistic equation. Regarding nonhyperbolic transitions we discuss a four-dimensional relaxation oscillation and also canard-like solutions emerging from the mo...

The paper presented a transient population dynamics of phase singularities in 2D Beeler-Reuter model. Two stochastic modelings are examined: (i) the Master equation approach with the transition rate (i.e., λ(n, t) = λ(t)n and μ(n, t) = μ(t)n) and (ii) the nonlinear Langevin equation approach with a multiplicative noise. The exact general solution of the Master equation with arbitrary time-depen...

A new sigmoid growth equation is presented for curve-fitting, analysis and simulation of growth curves. Like the logistic growth equation, it increases monotonically, with both upper and lower asymptotes. Like the Richards growth equation, it can have its maximum slope at any value between its minimum and maximum. The new sigmoid equation is unique because it always tends towards exponential gr...