Attractors with controllable basin sizes from cooperation of contracting and expanding dynamics in pulse-coupled oscillators<xref rid="cpb_28_1_010502fn1" ref-type="fn">*</xref> <fn id="cpb_28_1_010502fn1"> <label>*</label> <p>Project supported by the National Natural Science Foundation of China (Grant Nos. 11502200 and 91648101) and the Fundamental Research Funds for the Central Universities, China (Grant No. 3102018zy012).</p> </fn>

Attractors with controllable basin sizes from cooperation of contracting and expanding dynamics in pulse-coupled oscillators* *

Project supported by the National Natural Science Foundation of China (Grant Nos. 11502200 and 91648101) and the Fundamental Research Funds for the Central Universities, China (Grant No. 3102018zy012).

Zou Hai-Lin^†, Deng Zi-Chen

(a)–(c) The staying time for an unstable attractor is controlled. The staying time (highlighted in gray) becomes longer by decreasing B. (d) For the leaving process in (c), the evolution of phase difference for two active oscillators with time n reveals two processes with two different evolution rates as predicted. The parameters are N = 15, b = 3, ε = 0.1, τ = 0.1, and c = 10⁻⁴. The time n denotes the n-th reset of the reference oscillator 1.