  In a recent paper, we presented an intelligent evolutionary search technique
through genetic programming (GP) for finding new analytical expressions of
nonlinear dynamical systems, similar to the classical Lorenz attractor's which
also exhibit chaotic behaviour in the phase space. In this paper, we extend our
previous finding to explore yet another gallery of new chaotic attractors which
are derived from the original Lorenz system of equations. Compared to the
previous exploration with sinusoidal type transcendental nonlinearity, here we
focus on only cross-product and higher-power type nonlinearities in the three
state equations. We here report over 150 different structures of chaotic
attractors along with their one set of parameter values, phase space dynamics
and the Largest Lyapunov Exponents (LLE). The expressions of these new
Lorenz-like nonlinear dynamical systems have been automatically evolved through
multi-gene genetic programming (MGGP). In the past two decades, there have been
many claims of designing new chaotic attractors as an incremental extension of
the Lorenz family. We provide here a large family of chaotic systems whose
structure closely resemble the original Lorenz system but with drastically
different phase space dynamics. This advances the state of the art knowledge of
discovering new chaotic systems which can find application in many real-world
problems. This work may also find its archival value in future in the domain of
new chaotic system discovery.
