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- W1982210304 abstract "We develop two algorithms for obtaining an index 1 saddle torus between two attractors of which basin boundary is smooth by using the bisection method. In the first algorithm, which we name overall template method, we make a template approximating a whole attractor and use it for pattern matching. The attractor can be a periodic orbit, a torus and even a chaos. In the second algorithm, which we name partial template method, we make a template approximating only a part of an attractor. In this algorithm, the attractor is restricted to a periodic orbit and a two-torus, but calculation time is much smaller than that of the overall template method. We demonstrate these two algorithms for two solutions, observed in a ring of six-coupled bistable oscillators. One is a saddle torus in the basin boundary of the two switching solutions, and the other is of the two quasi-periodic propagating wave solutions. We calculate the Lyapunov spectrum of the obtained saddle torus, and confirm one positive Lyapunov exponent." @default.
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- W1982210304 date "2013-09-01" @default.
- W1982210304 modified "2023-09-27" @default.
- W1982210304 title "ALGORITHMS FOR OBTAINING A SADDLE TORUS BETWEEN TWO ATTRACTORS" @default.
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- W1982210304 doi "https://doi.org/10.1142/s0218127413300322" @default.
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