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Mathematical Problems in Engineering
Volume 2015, Article ID 508061, 6 pages
http://dx.doi.org/10.1155/2015/508061
Research Article

Mixed-Mode Oscillations in Nonautonomous Modified Chua’s Circuit

Department of Physics, Faculty of Science, Jiangsu University, Zhenjiang 212013, China

Received 6 April 2015; Revised 23 May 2015; Accepted 26 May 2015

Academic Editor: Gisele Mophou

Copyright © 2015 Ying Ji et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. G. V. Savino and C. M. Formigli, “Nonlinear electronic circuit with neuron like bursting and spiking dynamics,” BioSystems, vol. 97, no. 1, pp. 9–14, 2009. View at Publisher · View at Google Scholar · View at Scopus
  2. V. K. Vanag, L. Yang, M. Dolnik, A. M. Zhabotinsky, and I. R. Epstein, “Oscillatory cluster patterns in a homogeneous chemical system with global feedback,” Nature, vol. 406, no. 6794, pp. 389–391, 2000. View at Publisher · View at Google Scholar · View at Scopus
  3. T. Hayashi, “Mixed-mode oscillations and chaos in a glow discharge,” Physical Review Letters, vol. 84, no. 15, pp. 3334–3337, 2000. View at Publisher · View at Google Scholar · View at Scopus
  4. F. Zhang, A. Lubbe, Q. Lu, and J. Su, “On bursting solutions near chaotic regimes in a neuron model,” Discrete and Continuous Dynamical Systems, Series S, vol. 7, no. 6, pp. 1363–1383, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  5. W. Marszalek and Z. Trzaska, “Memristive circuits with steady-state mixed-mode oscillations,” Electronics Letters, vol. 50, no. 18, pp. 1275–1277, 2014. View at Publisher · View at Google Scholar
  6. T. M. Massoud and T. K. Horiuchi, “A neuromorphic VLSI head direction cell system,” IEEE Transactions on Circuits and Systems. I. Regular Papers, vol. 58, no. 1, pp. 150–163, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. A. Basu, S. Ramakrishnan, C. Petre, S. Koziol, S. Brink, and P. E. Hasler, “Neural dynamics in reconfigurable silicon,” IEEE Transactions on Biomedical Circuits and Systems, vol. 4, no. 5, pp. 311–319, 2010. View at Publisher · View at Google Scholar · View at Scopus
  8. J. V. Arthur and K. A. Boahen, “Silicon-neuron design: a dynamical systems approach,” IEEE Transactions on Circuits and Systems. I. Regular Papers, vol. 58, no. 5, pp. 1034–1043, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. H. Soleimani, A. Ahmadi, and M. Bavandpour, “Biologically inspired spiking neurons: piecewise linear models and digital implementation,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 59, no. 12, pp. 2991–3004, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. J. Rinzel, “Bursting oscillations in an excitable membrane model,” in Ordinary and Partial Differential Equations, B. D. Sleeman and R. J. Jarvis, Eds., vol. 1151 of Lecture Notes in Mathematics, pp. 304–316, Springer, Berlin, Germany, 1985. View at Publisher · View at Google Scholar
  11. A. Sherman and J. Rinzel, “Rhythmogenic effects of weak electrotonic coupling in neuronal models,” Proceedings of the National Academy of Sciences of the United States of America, vol. 89, no. 6, pp. 2471–2474, 1992. View at Publisher · View at Google Scholar · View at Scopus
  12. P. Smolen, D. Terman, and J. Rinzel, “Properties of a bursting model with two slow inhibitory variables,” SIAM Journal on Applied Mathematics, vol. 53, no. 3, pp. 861–892, 1993. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. E. M. Izhikevich, “Neural excitability, spiking and bursting,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 10, no. 6, pp. 1171–1266, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  14. Z. Q. Yang and Q. S. Lu, “Different types of bursting in Chay neuronal model,” Science in China, Series G: Physics, Mechanics and Astronomy, vol. 51, no. 6, pp. 687–698, 2008. View at Publisher · View at Google Scholar · View at Scopus
  15. G.-Q. Zhong, “Implementation of Chua's circuit with a cubic nonlinearity,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 41, no. 12, pp. 934–941, 1994. View at Publisher · View at Google Scholar · View at Scopus