Chaos in fractional conjugate Lorenz system and its scaling attractors

Chaotic dynamics of fractional conjugate Lorenz system are demonstrated in terms of local stability and largest Lyapunov exponent. Chaos does exist in the fractional conjugate Lorenz system with order less than three since it has positive largest Lyapunov exponent. Furthermore, scaling chaotic attractors of fractional conjugate Lorenz system is theoretically and numerically analyzed with the help of one-way synchronization method and adaptive synchronization method. Numerical simulations are performed to verify the theoretical analysis.