Work

The Verhulst-Like Equations: Integrable OΔE and ODE with Chaotic Behavior

Year: 2019

Type: article

Abstract: In this paper, we study various variants of Verhulst-like ordinary differential equations (ODE) and ordinary difference equations (O Δ E). Usually Verhulst ODE serves as an example of a deterministic system and discrete logistic equation is a classic example of a simple system with very complicated (chaotic) behavior. In our paper we present examples of deterministic discretization and chaotic continualization. Continualization procedure is based on Padé approximants. To correctly characterize the dynamics of obtained ODE we measured such characteristic parameters of chaotic dynamical systems as the Lyapunov exponents and the Lyapunov dimensions. Discretization and continualization lead to a change in the symmetry of the mathematical model (i.e., group properties of the original ODE and O Δ E). This aspect of the problem is the aim of further research.

Source: Symmetry

DOI: 10.3390/sym11121446

Authors: Igor Andrianov, Galina Starushenko, Sergey Kvitka, Lelya Khajiyeva

Institutions: RWTH Aachen University, National Academy for Public Administration under the President of Ukraine, Al-Farabi Kazakh National University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,418

OpenAlex ID: W2990120004

FWCI: 1.056

Cites: 17

Cited by: 7

Related to: 10