The conjoining of dynamical systems and deep learning has become a topic of great
interest. In particular, neural differential equations (NDEs) demonstrate that neural networks …

Stochastic differential equations (SDEs) are a staple of mathematical modelling of temporal
dynamics. However, a fundamental limitation has been that such models have typically been …

Data generated in postharvest research are characterised by an inherent large amount of
biological variance. This variance generally obscures the behaviour of interest, complicating …

In this paper we propose the numerical solutions of stochastic initial value problems via
random Runge–Kutta methods of the second order and mean square convergence of these …

Considering that the population size is always influenced by various uncertain factors in
varying environment, we present some new types of uncertain population models: uncertain …

A stochastic predator–prey system with Holling II functional response is proposed and
investigated. We show that there is a unique positive solution to the model for any positive …

The main aim of this study is to propose a numerical iterative approach for obtaining
approximate solutions of nonlinear stochastic Itô–Volterra integral equations. The method is …

In this paper we develop stochastic differential equation models for tumor population growth
with immunization. We investigate especially the effect of a multiplicative noise on the …

Stochastic differential equations (SDEs) have been widely used to model real world random
phenomena. Existing works mainly focus on the case where the time series is modeled by a …

City-level CO 2 emission scenarios are important for cities' policies of emission reduction.
However, current studies do not reveal the macro patterns of the evolution of cities. This …