Implementation of bidirectional chaotic communication systems based on Lorenz circuits

Circuit Implementation and Synchronization Control of Chaotic Horizontal Platform Systems by Wireless Sensors

“…Recently, many control technologies were also used to implement two identical chaotic systems to achieve synchronization, such as adaptive control, feedback control, sliding mode control and fuzzy sliding mode control [2]. However, elucidating or controlling the non-linear behavior of mechanical systems is extremely difficult, necessitating the use of electronic components to replace mechanical systems produced by nonlinear behavior [3,4].…”

Master–slave synchronization of continuously and intermittently coupled sampled-data chaotic oscillators

“…Synchronization schemes for two identical chaotic oscillators can be classified into bidirectional [16][17][18] and unidirectional [19][20][21][22][23] depending on the coupling between the oscillators [24]. Synchronization of unidirectionally coupled oscillators is generally referred to as master-slave synchronization.…”

A simple Lorenz circuit and its radio frequency implementation

“…9 However, the Lorenz equations have been implemented electronically by various authors using audio frequency components. 1,[10][11][12][13][14][15] Typically, these circuits contain several operational amplifiers, which perform linear operations ͑e.g., integration and summation͒, as well as a couple of integrated circuits that perform the nonlinear operations ͑i.e., multiplication͒. The relatively large number of active components makes it difficult to directly generalize these designs to high frequencies.…”

“…First, linear mathematical operations are not performed by the opera-tional amplifiers commonly used in audio frequency Lorenz circuits. 1,[10][11][12][13][14][15] Rather, summation is performed by adding currents at nodes according to Kirchoff's current law and integration is performed by charging the capacitors. Since summation is performed on currents, the voltage outputs of the multipliers must be converted into currents; thus, the second design choice is to configure the analog multipliers as current output devices.…”

“…The time scale of the oscillations is ϳ10 s, an order of magnitude faster than previous audio frequency Lorenz circuits. 1,[10][11][12][13][14][15] Close comparison of the time series in Figs. 3͑a͒ and 3͑b͒ reveals the fact that circuit A oscillates slightly slower than predicted by the model.…”