Title: Lyapunov Spectrum in a Four-Coupled Rössler Oscillator
Abstract: A four-coupled Rössler oscillator system is investigated. Various phases shown such as asynchronized, partially synchronized, intermittency and completely synchronized states appear as the coupling strength varies. Lyapunov spectrum is calculated for this system. The number of positive Lyapunov exponents decreases as synchronization becomes to be strong. Only one positive exponent exists in the completely synchronized state. The phase transitions occur when the value of second or third exponent changes from zero to negative. Time variation of Lyapunov exponents that take the values near zero plays an important role for intermittency states.