A Modified Quadratic Lorenz attractor

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.