A Modified Quadratic Lorenz attractor

TL;DR

This paper presents a modified quadratic Lorenz attractor, analyzing its chaotic properties through equilibria, eigenvalues, Lyapunov exponents, and numerical simulations, including multiplicative system forms and Runge-Kutta methods.

Contribution

It introduces a new chaotic system, the modified quadratic Lorenz attractor, with detailed analysis and simulation methods, expanding understanding of chaotic dynamics.

Findings

The system exhibits chaotic behavior confirmed by Lyapunov exponents.

Numerical simulations demonstrate complex attractor structures.

The multiplicative form allows alternative simulation approaches.

Abstract

This study introduces a modified quadratic Lorenz attractor. The properties of this new chaotic system are analysed and discussed in detail, by determining the equilibria points, the eigenvalues of the Jacobian, and the Lyapunov exponents. The numerical simulations, the time series analysis, and the projections to the $xy$-plane, $xz$-plane, and $yz$-plane are conducted to highlight the chaotic behaviour. The multiplicative form of the new system is also presented and the simulations are conducted using multiplicative Runge-Kutta methods.