**Author details**

**Figures 27** and **28** depict the phase portraits in (*xi*

314 Nonlinear Systems - Design, Analysis, Estimation and Control

method.

**7. Conclusion**

ronization behaviour.

, *yi*

7, *c* = 0.2 and *d* = 3, obtained from Cadence OrCAD. These figures confirm the achievement of complete synchronization in the case of unidirectionally coupled circuits with the proposed

**Figure 28.** The phase portrait of *y*2 versus *x*2, for *a* = 1, *B* = 7, *c* = 0.2 and *d* = 3, obtained from Cadence OrCAD.

In this chapter, the case of unidirectional coupling scheme of two chaotic non-autonomous dynamical systems was studied. The proposed system is the second order Birkhoff-Shaw system, which is simple but very interesting from the perspective of nonlinear analysis. Furthermore, the coupling method was based on a recently new proposed scheme based on the nonlinear controller, which is applied for the first time in non-autonomous systems.

The Birkhoff-Shaw system is one of the simplest 2-D nonlinear systems exhibiting a rich dynamical behaviour. Besides limit cycles, Birkhoff-Shaw system presents quasiperiodicity and chaos, which can make the control of the system a difficult target in practical applications, where a particular dynamic is desired. Also, two well-known phenomena of nonlinear theory, the Intermittency and the Interior Crisis have been observed. However, the main drawback of this system is the fact that this system is a non-autonomous dynamical system, which makes

In agreement to the simulation results, the circuital implementation of the proposed system in SPICE, in the case of unidirectional coupling, confirms the appearance of complete synchronization and antisynchronization, depending on the signs of the parameters of the error functions, in various cases. With this method, by choosing an appropriate sign for the error functions, the coupling system can be driven either to complete synchronization or antisynch-

the coupling method weak, especially if it is used in secure communication schemes.

) phase planes, with *i* = 1, 2, for *a* = 1, *B* =

Christos K. Volos1 , Hector E. Nistazakis2\*, Ioannis M. Kyprianidis1 , Ioannis N. Stouboulos1 and George S. Tombras2

\*Address all correspondence to: enistaz@phys.uoa.gr

1 Physics Department, Aristotle University of Thessaloniki, Thessaloniki, Greece

2 Department of Electronics, Computers, Telecommunications and Control, Faculty of Physics, National and Kapodistrian University of Athens, Athens, Greece
