Synchronization and oscillation quenching in coupled three nonidentical Lorenz oscillators

In this paper, we introduce the heterogeneity in the parameter s to three coupled Lorenz oscillators and investigate the effects of parameter heterogeneity on the coupling dynamics. In the presence of parameter heterogeneity, the complete synchronous state is replaced by lag synchronous state which owns the largest Lyapunov exponent exactly the same as that of the complete synchronous chaos. We find two types of oscillation quenching states induced by the parameter heterogeneity, homogeneous nontrivial equilibria and heterogeneous equilibria. In the homogeneous nontrivial equilibria, all oscillators fall onto a same nontrivial equilibrium of the isolated Lorenz oscillator, which requires low coupling strength. Depending on the coupling function, the heterogeneous equilibria may appear at intermediate coupling strength or large coupling strength. We numerically show that the transitions among lag synchronous state and different types of quenching states are always discontinuous ones. The stability diagram of the lag synchronous chaos is presented theoretically, which is compatible with those based on the synchronization error and Lyapunov exponents.