Bifurcations and multistability in a physically extended Lorenz system for rotating convection

We present a four-dimensional generalized Lorenz system for rotating weakly shear-thinning fluid layer subjected to heating from below. Various bifurcation patterns enroute to chaotic convection are reported. For certain parameter values, the system exhibits coexisting multiple attractors with different heterogeneous combinations viz., fixed point-periodic, multi-periodic with different periods, fixed point-chaotic, and periodic-chaotic depending upon initial conditions and system parameters. For basin of attraction corresponding to the coexisting attractors, both smooth and fractal basin boundaries can occur. The uncertainty fractional method is employed in exploring the fractality of the basin boundaries.