Anti-Phase and Inverse π-Lag Synchronization in Coupled Duffing-Type Circuits

The dynamic behavior of bidirectionally coupled Duffing-type circuits is numerically and experimentally investigated. Two related phenomena are explored such as anti-phase synchronization and inverse π-lag synchronization. Anti-phase synchronization is observed for the first time in coupled Duffing-type systems, while the inverse π-lag synchronization phenomenon in mutually coupled identical oscillators is a new type of synchronization. Inverse π-lag synchronization can be characterized by the vanishing of the sum of two relevant periodic signals. The first one is the signal of the first circuit x1 and the second is the signal of the second circuit x2 with a time lag τmin. This time lag is equal to T/2, where T is the period of x1 and x2. The measurements and numerical computations suggest that these two synchronization phenomena are correlated with the symmetry under the transformation, x → -x, y → -y and t → t + T/2, which the Duffing equation exhibits.

[1]  Bin Deng,et al.  Unidirectional synchronization of Hodgkin–Huxley neurons exposed to ELF electric field , 2009 .

[2]  Xin-Chu Fu,et al.  Projective Synchronization of Driving–Response Systems and Its Application to Secure Communication , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[3]  Ronnie Mainieri,et al.  Projective Synchronization In Three-Dimensional Chaotic Systems , 1999 .

[4]  E. Ott,et al.  Blowout bifurcations: the occurrence of riddled basins and on-off intermittency , 1994 .

[5]  J. A. Scott Kelso,et al.  Brain coordination dynamics: True and false faces of phase synchrony and metastability , 2009, Progress in Neurobiology.

[6]  Leon O. Chua,et al.  CONTROLLING AND SYNCHRONIZATION OF CHAOS IN THE SIMPLEST DISSIPATIVE NON-AUTONOMOUS CIRCUIT , 1995 .

[7]  P Woafo,et al.  Synchronized states in a ring of mutually coupled self-sustained electrical oscillators. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Leon O. Chua,et al.  EXPERIMENTAL CHAOS SYNCHRONIZATION IN CHUA'S CIRCUIT , 1992 .

[9]  Polina S. Landa,et al.  Synchronizing the chaotic oscillations by external force , 1991 .

[10]  Ioannis M. Kyprianidis,et al.  Synchronization of two resistively coupled nonautonomous and hyperchaotic oscillators , 2003 .

[11]  Ulrich Parlitz,et al.  Superstructure in the bifurcation set of the Duffing equation ẍ + dẋ + x + x3 = f cos(ωt) , 1985 .

[12]  Erik Mosekilde,et al.  Loss of synchronization in coupled Rössler systems , 2001 .

[13]  L. Chua,et al.  A UNIFIED FRAMEWORK FOR SYNCHRONIZATION AND CONTROL OF DYNAMICAL SYSTEMS , 1994 .

[14]  Jinghua Xiao,et al.  Antisynchronization in coupled chaotic oscillators , 2006 .

[15]  Shihua Chen,et al.  Lag synchronizing chaotic system based on a single controller , 2008 .

[16]  Arkady Pikovsky,et al.  On the interaction of strange attractors , 1984 .

[17]  Alexander S. Dmitriev,et al.  Ultrawideband wireless communications based on dynamic chaos , 2006 .

[18]  Christos Volos,et al.  Experimental demonstration of a chaotic cryptographic scheme , 2006 .

[19]  E. Mosekilde,et al.  Chaotic Synchronization: Applications to Living Systems , 2002 .

[20]  Kim-Fung Man,et al.  Uncertainty in Chaos Synchronization , 2001, Int. J. Bifurc. Chaos.

[21]  Nikolai F. Rulkov,et al.  Images of synchronized chaos: Experiments with circuits. , 1996, Chaos.

[22]  Dmitry E. Postnov,et al.  SYNCHRONIZATION OF CHAOS , 1992 .

[23]  Vadim S. Anishchenko,et al.  Antiphase Synchronization in symmetrically Coupled Self-oscillators , 2000, Int. J. Bifurc. Chaos.

[24]  Leon O. Chua,et al.  Transmission of Digital signals by Chaotic Synchronization , 1992, Chua's Circuit.

[25]  Spiegel,et al.  On-off intermittency: A mechanism for bursting. , 1993, Physical review letters.

[26]  Jinde Cao,et al.  Adaptive synchronization of a switching system and its applications to secure communications. , 2008, Chaos.

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

[28]  A. Pikovsky,et al.  Synchronization: Theory and Application , 2003 .

[29]  Parlitz,et al.  Experimental observation of phase synchronization. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[30]  H. Fujisaka,et al.  Stability Theory of Synchronized Motion in Coupled-Oscillator Systems , 1983 .

[31]  Ioannis M. Kyprianidis,et al.  Dynamics of Two resistively Coupled Duffing-Type Electrical oscillators , 2006, Int. J. Bifurc. Chaos.

[32]  E. Mosekilde,et al.  Chaotic Synchronization between Coupled Pancreatic β-Cells , 2000 .

[33]  Leon O. Chua,et al.  Experimental Demonstration of Secure Communications via Chaotic Synchronization , 1992, Chua's Circuit.

[34]  R. Yamapi,et al.  Chaos synchronization of resistively coupled Duffing systems: Numerical and experimental investigations , 2009 .

[35]  Gérard Bloch,et al.  Chaotic Cryptosystems: Cryptanalysis and Identifiability , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[36]  Amalia Miliou,et al.  Secure communication by chaotic synchronization: Robustness under noisy conditions , 2007 .

[37]  Ioannis M. Kyprianidis,et al.  On–off intermittent synchronization between two bidirectionally coupled double scroll circuits , 2010 .

[38]  Y. Ueda.  Randomly transitional phenomena in the system governed by Duffing's equation , 1978 .

[39]  L. Tsimring,et al.  Generalized synchronization of chaos in directionally coupled chaotic systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[40]  E. Mosekilde,et al.  Synchronization phenomena in nephron-nephron interaction. , 2001, Chaos.

[41]  Voss,et al.  Anticipating chaotic synchronization , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[42]  Guo-Hui Li.  Inverse lag synchronization in chaotic systems , 2009 .

[43]  M. Hasler,et al.  Effect of parameter mismatch on the mechanism of chaos synchronization loss in coupled systems , 1998 .

[44]  Young-Jai Park,et al.  Anti-synchronization of chaotic oscillators , 2003 .

[45]  J. Kurths,et al.  From Phase to Lag Synchronization in Coupled Chaotic Oscillators , 1997 .

[46]  Yanqiu Che,et al.  Chaos control and synchronization of two neurons exposed to ELF external electric field , 2007 .

[47]  Y. Lai,et al.  Observability of lag synchronization of coupled chaotic oscillators. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[48]  Hebertt Sira-Ramírez,et al.  Synchronization of Chaotic Systems: a generalized Hamiltonian Systems Approach , 2001, Int. J. Bifurc. Chaos.

[49]  Chai Wah Wu,et al.  A Simple Way to Synchronize Chaotic Systems with Applications to , 1993 .

[50]  Kurths,et al.  Phase synchronization of chaotic oscillators. , 1996, Physical review letters.

[51]  J. Fell,et al.  Memory formation by neuronal synchronization , 2006, Brain Research Reviews.

[52]  Y. Ueda.  Survey of regular and chaotic phenomena in the forced Duffing oscillator , 1991 .

[53]  Hiroshi Kawakami,et al.  Bifurcation Analysis of Current Coupled BVP oscillators , 2007, Int. J. Bifurc. Chaos.

[54]  L. Magafas,et al.  Digital Chaotic Synchronized Communication System , 2009 .

[55]  Paul Woafo,et al.  Chaotic synchronization with experimental application to secure communications , 2009 .

[56]  Guanrong Chen,et al.  Chaos synchronization of coupled neurons with gap junctions , 2006 .