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

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.