Simulation

A numerical simulation is a calculation that is run on a computer following a program that implements a mathematical model for a physical system. Numerical simulations are required to study the behaviour of systems whose mathematical models are too complex to provide analytical solutions, as in most nonlinear systems.

Period-doubling route

Bifurcation diagram

Pattern formation

Spatial distribution (arrangement) of the species

Hopf bifurcation in a fractional-ordered delayed system

Transition from chaotic to stable dynamics

Tools for detecting chaos in a system

MATLAB is a programming and numeric computing platform used by millions of engineers and scientists to analyze data, develop algorithms, and create models.

Wolfram Mathematica is a software system with built-in libraries for several areas of technical computing that allow machine learning, statistics, symbolic computation, manipulating matrices, plotting functions and various types of data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other programming languages.