This discovery stimulated extensive investigations of more complex hyperchaotic oscillators, generating signals with multiple PLEs. We have designed and investigated several sophisticated electronic oscillators, namely, higher order circuits, which involve combined resonance loops. Some of the hyperchaotic oscillators are characterized by not only multiple PLEs, but also by large metric entropy, which ensuring a high complexity of the signals. The instrument enables one to distinguish between secure and nonsecure chaotic signals. No matter how one proposes to exploit chaos or hyper-chaos in secure communications, the transmitter and receiver are usually required to be synchronized.
Most communication systems operate with only one transmitted signal.
Thus the main requirement for chaotic and especially the hyperchaotic oscillators is the capacity for achieving synchronization via a scalar transmitted signal or by means of a single dynamical variable. Several sophisticated techniques to synchronize hyperchaotic oscillators by means of a scalar signal have been proposed in the available literature. We have developed a novel approach based on the intentional design of hyperchaotic oscillators, which immediately admit synchronization via a single dynamical variable. In most cases, the problem of synchronization is considered numerically. One of them is based on the Krasovskii-Lyapunov theory, which is an extension of the second Lyapunov method for delay differential equations.