The amplitude death island of the delay-coupled system (6a) on the ( ) space for σ = 0.3 (a) and σ = 0.6 (b). The solid lines come from analyses, they show good agreement with the numerical results (black points) in both the subfigures. Here, we fix N = 100 and w 0 = 5.0.
(a) and (b) The normalized scaling factor R vs σ for w 0 = 2.3, 2.5 (solid circles and open circles) and w 0 = 4.0, 5.0 (solid squares and open squares), respectively. The data for the numerical simulation [scatter points] fit well with analytical result [solid line].
(a) Bifurcation diagram of the meaning field X(t) for the maximal (square points) and minimal (circular points) values with . (b) The normalized scaling factor R vs w 0 for σ = 0.6. The solid line which fits with the numerical results (open circles) well comes from analyses.
The time series of the meaning field for the different frequency are shown: w 0 = 5.0 ((a)–(b)) and w 0 = 2.3 ((c)–(d)); σ = 0.6. The others parameter sets: (a) ( ) (outside the amplitude death island) and (b) ( ) (inside the amplitude death island); (c) ( ) and (d) ( ) (they are chosen arbitrarily). The upper figures show a dramatic difference clearly between oscillatory state and amplitude death state after the transient, and the below figures indicate that amplitude death do not occur for the small frequency with the arbitrary values. The same random initial conditions are chosen.
The phase diagram for amplitude death region of delay-coupled chaotic system (16a) for σ = 0.0 (a), 0.05 (b), 0.1 (c), 0.15 (d). The solid lines represent the results from analyses.
The normalized scaling factor R vs σ.
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