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