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Pecora-Carroll synchronisation

Two Lorenz systems synchronise when the slave (y_s, z_s) subsystem is driven by the master's x and the conditional Lyapunov exponents of the receiver are negative. The error decays exponentially to zero.

σ: 10.00

ρ: 28.00

β: 2.667

Slave y₀ (mismatch): 10.00

Time horizon: 30

Pecora-Carroll synchronisation (1990)

master:  dx/dt = σ(y − x),  dy/dt = x(ρ − z) − y,  dz/dt = x y − β z
slave:                       dy_s/dt = x · (ρ − z_s) − y_s,
                              dz_s/dt = x · y_s − β z_s

The slave uses the master's x as the drive signal. Conditional Lyapunov
exponents of the (y_s, z_s) sub-system are negative, so |y_master − y_slave|
decays exponentially to zero. The receiver "locks on" to the chaotic master
state. Decoders for chaos-based communication exploit this.

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