Bidirectional Synchronization of Two IdenticalJerk Oscillators with Memristor

In this paper, the case of introducing memristor as a coupling component when synchronizing two identical simple chaotic oscillator (3-D Jerk equations) were observed. Also, the numerical simulation of the phase portraits are in good agreement with the MultiSIM and experimental simulations. Due to the complex chaotic dynamics of this oscillator, the realization of the electronic circuit involving two identical Jerk oscillator with memristor as coupling component were synchronized via bidirectional coupling and further applied to secure communication.

[1]  Alan V. Oppenheim,et al.  Circuit implementation of synchronized chaos with applications to communications. , 1993, Physical review letters.

[2]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[3]  Julien Clinton Sprott,et al.  Simplest dissipative chaotic flow , 1997 .

[4]  Vinod Patidar,et al.  Identical synchronization in chaotic jerk dynamical systems , 2006 .

[5]  L.O. Chua,et al.  Memristive devices and systems , 1976, Proceedings of the IEEE.

[6]  S. A. Tahir The Synchronization of Identical Memristors Systems Via Lyapunov Direct Method , 2013 .

[7]  Jack Heidel,et al.  ERRATUM: Non-chaotic behaviour in three-dimensional quadratic systems , 1997 .

[8]  Ioannis M. Kyprianidis,et al.  Fingerprint images encryption process based on a chaotic true random bits generator , 2010, Int. J. Multim. Intell. Secur..

[9]  J. C. Sprotta Some simple chaotic jerk functions , 1997 .

[10]  Chua Memristor-The Missing Circuit Element LEON 0 , 1971 .

[11]  S. Vaidyanathan,et al.  The Concept of Unidirectionally Coupled Nonlinear Circuits via a Memristor , 2012 .

[12]  Hyperchaos synchronization of memristor oscillator system via combination scheme , 2014 .

[13]  Julien Clinton Sprott,et al.  A New Chaotic Jerk Circuit , 2011, IEEE Transactions on Circuits and Systems II: Express Briefs.

[14]  Julien Clinton Sprott,et al.  A new class of chaotic circuit , 2000 .

[15]  Henry Leung,et al.  Design and implementation of n-scroll chaotic attractors from a general jerk circuit , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[16]  Ralf Eichhorn,et al.  Transformations of nonlinear dynamical systems to jerky motion and its application to minimal chaotic flows , 1998 .

[17]  Bharathwaj Muthuswamy,et al.  Implementing Memristor Based Chaotic Circuits , 2010, Int. J. Bifurc. Chaos.

[18]  Mustak E. Yalcin,et al.  Multi-scroll and hypercube attractors from a general jerk circuit using Josephson junctions , 2007 .

[19]  Rita McCardell Doerr,et al.  Generation , 2015, Aristotle on Substance.

[20]  N. Karadimas,et al.  Numerical Simulations in Jerk Circuit and It ’ s Application in a Secure Communication System , 2013 .