A COMPARATIVE ANALYSIS OF RÖSSLER TYPE DYNAMICS AND LASER SYSTEMS

We introduce the standard Rössler oscillator and extend it from a system defined on ℝ3 to a system defined on [Formula: see text]. We extend the system in such a way that the simple Rössler type dynamics are preserved, whilst introducing an additional symmetry to the system such that when the oscillators are linearly coupled, there exists an embedding of symmetry forced invariant manifolds. We contrast our results with a previously considered model for a linearly coupled solid-state laser system which possessed a similar embedding of invariant manifolds. We discuss whether the mechanisms for loss of synchronization are system dependent or a more generic property of systems with embedded invariant manifolds.