Thamilmaran, K.; Lakshmanan, M.; Venkatesan, A. Hyperchaos in a modified canonical Chua’s circuit. (English) Zbl 1067.94597 Int. J. Bifurcation Chaos Appl. Sci. Eng. 14, No. 1, 221-243 (2004). Summary: We present the hyperchaos dynamics of a modified canonical Chua’s electrical circuit. This circuit, which is capable of realizing the behavior of every member of the Chua’s family, consists of just five linear elements (resistors, inductors and capacitors), a negative conductor and a piecewise linear resistor. The route followed is a transition from regular behavior to chaos and then to hyperchaos through border-collision bifurcation, as the system parameter is varied. The hyperchaos dynamics, characterized by two positive Lyapunov exponents, is described by a set of four coupled first-order ordinary differential equations. This has been investigated extensively using laboratory experiments, Pspice simulation and numerical analysis. Cited in 66 Documents MSC: 94C05 Analytic circuit theory 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 37G25 Bifurcations connected with nontransversal intersection in dynamical systems 37C10 Dynamics induced by flows and semiflows Keywords:Chaos; hyperchaos; modified canonical Chua’s circuit; border-collision bifurcation PDFBibTeX XMLCite \textit{K. Thamilmaran} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 14, No. 1, 221--243 (2004; Zbl 1067.94597) Full Text: DOI References: [1] Banerjee S., Phys. Rev. 59 pp 4052– [2] Blakely J. N., Int. J. Bifurcation and Chaos 4 pp 835– [3] Chin W., Phys. Rev. 50 pp 4427– [4] DOI: 10.1109/31.55064 · Zbl 0706.94026 [5] DOI: 10.1109/31.76487 [6] Harrison M. A., Phys. Rev. 59 pp R3799– [7] DOI: 10.1143/PTP.69.1806 · Zbl 1200.37031 [8] DOI: 10.1142/S0218127494000356 · Zbl 0813.58037 [9] DOI: 10.1109/81.298367 [10] Kapitaniak T., Phys. Rev. 62 pp 1972– [11] Kyprianidis I. M., Phys. Rev. 52 pp 2268– [12] Kyprianidis I. M., Int. J. Bifurcation and Chaos 10 pp 1903– [13] DOI: 10.1142/9789812798701 [14] DOI: 10.1109/TCS.1985.1085791 · Zbl 0578.94023 [15] DOI: 10.1109/TCS.1986.1085862 [16] DOI: 10.1109/81.340840 · Zbl 0866.94036 [17] Nusse H. E., Phys. Rev. 49 pp 1073– [18] DOI: 10.1103/PhysRevLett.76.904 [19] DOI: 10.1103/PhysRevLett.74.1970 [20] Roberts W., SPICE (1997) [21] Rossler O. E., Phys. Lett. 71 pp 155– · Zbl 0996.37502 [22] Saito T., Electron. Commun. Japan 72 pp 58– [23] Stoop R., Physica 35 pp 425– [24] DOI: 10.1049/el:19960630 [25] DOI: 10.1049/el:19961357 [26] DOI: 10.1049/el:19970393 [27] Tamaševičius A., Electron. Lett. 33 pp 2205– [28] DOI: 10.1016/S0960-0779(97)00054-4 · Zbl 0935.37057 [29] Wolf A., Physica 16 pp 285– [30] DOI: 10.1109/81.246147 · Zbl 0844.58064 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.