# Abstract:

Hopf bifurcation, dynamics at infinity and robust modified function projective synchronization (RMFPS) problem for Sprott E system with quadratic perturbation were studied in this paper. By using the method of projection for center manifold computation, the subcritical and the supercritical Hopf bifurcation were analyzed and obtained. Then, in accordance with the Poincare compactification of polynomial vector field in $R^3$, the dynamical behaviors at infinity were described completely. Moreover, a RMFPS scheme of this special system was proposed and proved based on Lyapunov direct method. The simulation results demonstrate the correctness of the dynamics analysis and the effectiveness of the proposed synchronization strategy.

# Keywords:

Hopf bifurcation, center manifold theorem, Poincare compactification, robust modified function projective synchronization, chaotic systems

# Classification:

34H10, 34H20, 93C15

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