Chaos Synchronization — Coupled Rössler Systems

Complete synchronization · conditional Lyapunov exponents · Pecora-Carroll 1990

Coupling

Synchronization error:
Not synchronized
Pecora-Carroll 1990: Two identical chaotic systems can synchronize when unidirectionally coupled. Condition: all conditional Lyapunov exponents of the driven subsystem must be negative.

Rössler attractor: ẋ=−y−z, ẏ=x+ay, ż=b+z(x−c)

Complete sync: x₁(t)→x₂(t) exponentially. Parameter mismatch creates "imperfect" sync.

Pink = drive system, green = response. Bottom: synchronization error x₁−x₂