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Xiao Bao Lin, NC State, Chaotic Traveling Wave Solutions In Coupled Circuits
September 13, 2017 | 3:00 pm - 4:00 pm EDT
Coupled array of Chua’s circuits has been studied for many years.
Some experimental and numerical study of traveling waves were conducted
by Perez and Chua in 1993. Existence of periodic traveling waves were proved
by S.-N. Chow, M. Jiang and X.-B. Lin in 2013.
Some experimental and numerical study of traveling waves were conducted
by Perez and Chua in 1993. Existence of periodic traveling waves were proved
by S.-N. Chow, M. Jiang and X.-B. Lin in 2013.
This talk is based on a joint work with F. Geng and X. Liu.
We have proved the existence of chaotic traveling wave solutions in three steps.
1. We show that the ODE system for traveling waves can have
a heteroclinic loop consisting of two traveling waves moving with
the same speed.
2. At each equilibrium point of the heteroclinic loop, the system
has a pair of complex eigenvalues with negative real parts.
3. From Shil’nikov’s theorem of symbolic dynamics, the system
can have chaotic solutions near the traveling heteroclinic orbits.