Related papers: A note on differential equations of logistic type
The logistic function is shown to be solution of the Riccati equation, some second-order nonlinear ordinary differential equations and many third-order nonlinear ordinary differential equations. The list of the differential equations having…
In this paper we introduce and investigate a new kind of functional (including ordinary and evolutionary partial) differential equations. The main goal of this paper is to explore our new philosophy by some examples on functional ODEs and…
A functional differential equation related to the logistic equation is studied by a combination of numerical and perturbation methods. Parameter regions are identified where the solution to the nonlinear problem is approximated well by…
This work is devoted to find the numerical solutions of several one dimensional second-order ordinary differential equations. In a heuristic way, in such equations the quadratic logistic maps regarded as a local function are inserted within…
Two types of population models are well known -- the continuous and the discrete types.The two have very different characteristics and methods of solutions and analysis.In this note, we point out that an iterative technique when applied to…
A nonlinear inequality is formulated in the paper. An estimate of the rate of growth/decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can…
An analysis of a fractional cubic differential equation is presented, which is a generalization of different versions of fractional logistic equations, in order to obtain simpler numerical methods that globalize and extend the results…
This paper investigates a nonlinear logistic model for age-structured population dynamics. The model incorporates interdependent fertility and mortality functions within a logistic framework, offering insights into stationary solutions and…
Here we study the abstract nonlinear differential equation of second order that in special case is the equation of the type of equation of traffic flow. We prove the solvability theorem for the posed problem under the appropriate conditions…
Integral operators play an important role modeling various physical and biological processes. In this article we consider such a nonlinear integro-differential equation. We study several properties of equilibrium solutions of the operator…
In the present paper we propose a new approach to investigate the logistic function, commonly used in mathematical models in economics and management. The approach is based on indicating in a given time series, having a logistic trend, some…
Many real-world scientific processes are governed by complex nonlinear dynamic systems that can be represented by differential equations. Recently, there has been increased interest in learning, or discovering, the forms of the equations…
The logistic equation is ubiquitous in applied mathematics as a minimal model of saturating growth. Here, we examine a broad generalisation of the logistic growth model to discretely structured populations, motivated by examples that range…
Effort has been given for the development of an analytical approach that helps to address several sigmoidal and non-sigmoidal growth processes found in literature. In the proposed approach, the role of specific growth rate in different…
In this work we systematically analyze general properties of differential equations used as machine learning models. We demonstrate that the gradient of the loss function with respect to to the hidden state can be considered as a…
This note is designed to show some classes of differential-difference equations admitting Lax representation which generalize evolutionary equations known in the literature.
We show how machine learning methods can unveil the fractional and delayed nature of discrete dynamical systems. In particular, we study the case of the fractional delayed logistic map. We show that given a trajectory, we can detect if it…
We study a class of evolutionary partial differential systems with two components related to second order (in time) non-evolutionary equations of odd order in spatial variable. We develop the formal diagonalisation method in symbolic…
We use comparison principles, variational arguments and a truncation method to obtain positive solutions to logistic type equations with harvesting both in $\mathbb{R}^N$ and in a bounded domain $\Omega\subset\mathbb{R}^N$, with $N\geq 3$,…
Spatial evolutionary games model individuals who are distributed in a spatial domain and update their strategies upon playing a normal form game with their neighbors. We derive integro-differential equations as deterministic approximations…