Systems, methods, apparatus, and techniques are presented for maintaining cupolets in a state of mutual stabilization. A first cupolet and a second cupolet are generated. A first control code is applied to the first cupolet for a first time to produce a first visitation code. The first visitation code is transformed based on an exchange function to produce a second control code. The second control code is applied to the second cupolet to produce a second visitation code. The second visitation code is transformed based on the exchange function to produce the first control code. The first control code is applied to the first cupolet for a second time.