Symmetrical Turing instability in Chua corsage memristor siblings-based two-cell network

doi:10.1088/1674-1056/ae68f9

Abstract The Turing instability, a counterintuitive phenomenon in which two quiescent cells lose stability when coupled through a dissipative environment, has been explained via the edge of chaos theory. While the classical Turing instability and its local form have been recently elucidated, its symmetrical form — a distinct class of symmetry-breaking phenomena wherein two identical cells, each poised at a mirror-symmetrical stable operating point, undergo destabilization and bifurcate into two distinct mirror-symmetrical stable states under opposite bias voltages — has not been reported yet. This paper introduces a current-controlled odd-symmetrical Chua corsage memristor (OS-CCM) and employs it to investigate the symmetrical Turing instability in a resistively coupled two-cell network. Coupling two identical bistable OS-CCM-based cells, each originally poised at identical mirror-symmetrical stable states, via a passive resistor destabilizes their original stability, giving rise to two distinct stable states and ultimately leading to quadristability, referring to a dynamical phenomenon with four coexisting stable states, which demonstrates the emergence of symmetrical Turing instability. The quantitative condition for the emergence of this phenomenon is analytically derived and precisely determined through eigenvalue analysis. Both numerical simulations and hardware experiments confirm the correctness of the theoretical analysis.

Keywords: Chua corsage memristor local activity edge of chaos destabilization symmetrical Turing instability

Received: 16 February 2026
Revised: 03 April 2026
Accepted manuscript online: 06 May 2026

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	82.40.Bj	(Oscillations, chaos, and bifurcations)
	87.19.ll	(Models of single neurons and networks)

Fund: This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 62501213 and 62574072), Zhejiang Provincial Natural Science Foundation of China (Grant No. LQN25F010008), and the Fundamental Research Funds for the Provincial Universities of Zhejiang (Grant No. GK249909299001-025).

Corresponding Authors: Peipei Jin
E-mail: jinpeipei@hdu.edu.cn

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Zhicheng Tian(田桎成), Peipei Jin(靳培培), Shutong Liu(刘姝彤), Meiyuan Gu(顾梅园), Long Chen(陈龙), and Guangyi Wang(王光义) Symmetrical Turing instability in Chua corsage memristor siblings-based two-cell network 2026 Chin. Phys. B 35 060511

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[1]	Frequency-tunable spiking dynamics of Chua corsage memristors Qijian Wu(吴奇键), Peipei Jin(靳培培), Xiameng Wu(吴夏萌), Meiyuan Gu(顾梅园), Wei Zhou(周玮), Yujiao Dong(董玉姣), Yan Liang(梁燕), and Long Chen(陈龙). Chin. Phys. B, 2026, 35(4): 048703.
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Symmetrical Turing instability in Chua corsage memristor siblings-based two-cell network

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