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In this work, the dynamics of a system of mutually coupled Generalized Lorenzsystems (GLS) is investigated. The state variables of two Lorenz oscillatorsare coupled mutually via non-linear controls and synchronization is achievedbetween the state variables. We find that by suitably controlling a parameterhaving a bearing on the coupling coefficient between the two Lorenzoscillators, the GLS, while preserving synchronization is rendered to a statewherein chaotic nature of state variables is suppressed and state variablesexhibit oscillatory character. The suppression of chaos is verified by powerspectra, permutation entropy and Lyapunov exponent calculations. When operatedin chaotic domain, we show the possibility of transition from the state ofsynchronization to the state of anti-synchronization.

Suppression of Chaos in Mutually Coupled Synchronized Generalized Lorenz Systems