Srinivasan, K.; Senthilkumar, D. V.; Murali, K.; Lakshmanan, M.; Kurths, J. Synchronization transitions in coupled time-delay electronic circuits with a threshold nonlinearity. (English) Zbl 1317.34111 Chaos 21, No. 2, 023119, 11 p. (2011). Summary: Experimental observations of typical kinds of synchronization transitions are reported in unidirectionally coupled time-delay electronic circuits with a threshold nonlinearity and two time delays, namely feedback delay \(\tau_1\) and coupling delay \(\tau_2\). We have observed transitions from anticipatory to lag via complete synchronization and their inverse counterparts with excitatory and inhibitory couplings, respectively, as a function of the coupling delay \(\tau_2\). The anticipating and lag times depend on the difference between the feedback and the coupling delays. A single stability condition for all the different types of synchronization is found to be valid as the stability condition is independent of both the delays. Further, the existence of different kinds of synchronizations observed experimentally is corroborated by numerical simulations and from the changes in the Lyapunov exponents of the coupled time-delay systems.{©2011 American Institute of Physics} Cited in 14 Documents MSC: 34C60 Qualitative investigation and simulation of ordinary differential equation models 34C28 Complex behavior and chaotic systems of ordinary differential equations 34D06 Synchronization of solutions to ordinary differential equations PDFBibTeX XMLCite \textit{K. Srinivasan} et al., Chaos 21, No. 2, 023119, 11 p. (2011; Zbl 1317.34111) Full Text: DOI arXiv References: [1] DOI: 10.1103/PhysRevLett.79.2911 · doi:10.1103/PhysRevLett.79.2911 [2] DOI: 10.1103/PhysRevLett.85.3381 · doi:10.1103/PhysRevLett.85.3381 [3] DOI: 10.1103/PhysRevLett.100.144102 · doi:10.1103/PhysRevLett.100.144102 [4] DOI: 10.1103/PhysRevE.74.035204 · doi:10.1103/PhysRevE.74.035204 [5] DOI: 10.1103/PhysRevLett.92.144101 · doi:10.1103/PhysRevLett.92.144101 [6] DOI: 10.1103/PhysRevLett.94.134102 · doi:10.1103/PhysRevLett.94.134102 [7] DOI: 10.1103/PhysRevLett.92.074104 · doi:10.1103/PhysRevLett.92.074104 [8] DOI: 10.1038/nature04275 · doi:10.1038/nature04275 [9] DOI: 10.1063/1.2937120 · Zbl 06417157 · doi:10.1063/1.2937120 [10] DOI: 10.1063/1.3096411 · Zbl 06437636 · doi:10.1063/1.3096411 [11] DOI: 10.1103/PhysRevA.64.013805 · doi:10.1103/PhysRevA.64.013805 [12] DOI: 10.1103/PhysRevE.66.026218 · doi:10.1103/PhysRevE.66.026218 [13] DOI: 10.1103/PhysRevLett.88.174101 · doi:10.1103/PhysRevLett.88.174101 [14] DOI: 10.1063/1.1485127 · doi:10.1063/1.1485127 [15] DOI: 10.1103/PhysRevE.68.016215 · doi:10.1103/PhysRevE.68.016215 [16] DOI: 10.1103/PhysRevE.67.026220 · doi:10.1103/PhysRevE.67.026220 [17] DOI: 10.1103/PhysRevLett.97.123902 · doi:10.1103/PhysRevLett.97.123902 [18] DOI: 10.1103/PhysRevLett.96.024102 · doi:10.1103/PhysRevLett.96.024102 [19] DOI: 10.1103/PhysRevLett.104.114102 · doi:10.1103/PhysRevLett.104.114102 [20] DOI: 10.1103/PhysRevLett.87.154101 · doi:10.1103/PhysRevLett.87.154101 [21] DOI: 10.1103/PhysRevLett.90.194101 · doi:10.1103/PhysRevLett.90.194101 [22] DOI: 10.1142/S0218127402005340 · doi:10.1142/S0218127402005340 [23] DOI: 10.1103/PhysRevE.75.016207 · doi:10.1103/PhysRevE.75.016207 [24] DOI: 10.1103/PhysRevE.74.016211 · doi:10.1103/PhysRevE.74.016211 [25] DOI: 10.1063/1.2737820 · Zbl 1159.37401 · doi:10.1063/1.2737820 [26] DOI: 10.1063/1.2737820 · Zbl 1159.37401 · doi:10.1063/1.2737820 [27] DOI: 10.1103/PhysRevE.74.035205 · doi:10.1103/PhysRevE.74.035205 [28] DOI: 10.1103/PhysRevE.71.016211 · doi:10.1103/PhysRevE.71.016211 [29] DOI: 10.1063/1.3125721 · Zbl 1309.34105 · doi:10.1063/1.3125721 [30] DOI: 10.1063/1.3125721 · Zbl 1309.34105 · doi:10.1063/1.3125721 [31] DOI: 10.1103/PhysRevLett.87.014102 · doi:10.1103/PhysRevLett.87.014102 [32] DOI: 10.1103/PhysRevLett.87.014102 · doi:10.1103/PhysRevLett.87.014102 [33] DOI: 10.1103/PhysRevLett.86.2782 · doi:10.1103/PhysRevLett.86.2782 [34] DOI: 10.1016/S0378-4371(01)00362-4 · Zbl 0973.37033 · doi:10.1016/S0378-4371(01)00362-4 [35] DOI: 10.1103/PhysRevE.65.036202 · doi:10.1103/PhysRevE.65.036202 [36] DOI: 10.1103/PhysRevLett.101.078102 · doi:10.1103/PhysRevLett.101.078102 [37] DOI: 10.1103/PhysRevE.81.045201 · doi:10.1103/PhysRevE.81.045201 [38] DOI: 10.1016/0167-2789(82)90042-2 · Zbl 1194.37052 · doi:10.1016/0167-2789(82)90042-2 [39] DOI: 10.1103/PhysRevE.58.3067 · doi:10.1103/PhysRevE.58.3067 [40] DOI: 10.1103/PhysRevE.58.3067 · doi:10.1103/PhysRevE.58.3067 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.