Chua's circuit with a slow-fast effect is established under certain parameter conditions. The dynamics of this slow-fast system is investigated. A spiking phenomenon can be observed in the numerical simulation. By introducing slow-fast analysis and a generalized Jacobian matrix at the non-smooth boundaries, the bifurcation mechanism for the periodic spiking solution, different from the smooth case, is discussed.
Chua's circuit with a slow-fast effect is established under certain parameter conditions. The dynamics of this slow-fast system is investigated. A spiking phenomenon can be observed in the numerical simulation. By introducing slow-fast analysis and a generalized Jacobian matrix at the non-smooth boundaries, the bifurcation mechanism for the periodic spiking solution, different from the smooth case, is discussed.
[1] Sparrow C 1982 The Lorenz Equations: Bifurcation, Chaos and Strange Attractor (New York: Springer) [2] Rossler O E 1976 Phys. Lett. A 57 397 [3] Chua L O and Lin G N 1990 IEEE Trans. Circ. Syst. 37 885 [4] Carroll T L and Pecora L M 1991 IEEE Trans. Circ. Syst. 38 453 [5] Suykens J A K, Huang A and Chua L O 1997 Achivfur Elektronik und Ubertragungstechnik 51 131 [6] Izhikevich E M 2000 Int. J. Bifur. Chaos 6 1171 [7] Ji Y and Bi Q S 2010 Phys. Lett. A 374 1434 [8] Lin W and He Y B 2005 Chaos 15 023705 [9] Leine R I and Campen D H 2006 European J. Mechanics A/Solids 25 595
2010, Vol. 27 
