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

An original unstable attractor with oscillators 6 and 7 as the active firing oscillators is successfully controlled to be a stable attractor marked by “+”. The red region denotes its basin, where the basin size is correctly predicted as shown by the dashed line. The nearby point within the basin leads to the stable attractor as shown in green ◀, while the nearby point outside the basin leaves the stable attractor as shown in yellow ⋆. The parameters are chosen as N = 15, b = 3, ε = 0.2, B = 5, and c = 10⁻⁴.