The control of a memory cell with the multiple stable states

Variations of Boundary Surface in Chua’s Circuit

“…Knowledge of the separatrix could be used not only in the binary memory described by the set of two (m = 2) differential equations, but also in the m-dimensional state space (m 3) or at a later analysis (now using the computers) of multiple valued (MV) memory at m = 3 [11][12][13][14][15][16][17]. In addition, knowledge of BS not only enables to design optimal parameters of controlling impulse of MV memory [16], but also to explain the failure of the memory -not only in the presence of stable limit cycles (SLCs), but also in their absence in case of virtual saddle point [14], [19][20][21]. This is another reason for interest in BS and its engineering usage.…”

Boundary surface and stable manifold in sequential circuits

“…However, when cross sections were made through the unstable singularities N1, N2, it turned out that at C=10fF (Fig.2) BS does not pass through the saddle point N1 (BS does not separate attractors S1 and S2), as it is for C=20fF (Fig.3) to 260fF. IV characteristics of the element and the load in Fig.2a or Fig.3a in i,u2 plane correspond to parameters listed in Table 1 [17]. IV characteristics in plane u1,u2 when R = 0 are projected as the line, Fig.2b or Singularities S1, S2 and S3 are stable and N1, N2 are unstable -according to Table 1, the conventional saddle points.…”

“…Description of the circuit by differential equations and its parameters can be found in [17] in this proceedings, in the Introduction chapter. In the next section of this item we will consider supply voltage U=440mV, control pulse I=0, R=0, L=100pH and C=C 1 =C 2 .…”

“…In [18], the case was shown where the circuit in Fig.1 was characterized for the parameters listed in Table 1 [17] and C=500fF, except the three stable singularities, also by other three undesirable stable limit cycles (SLC). Their presence caused a malfunction of the analyzed memory.…”

“…There were cross sections of BS made in u 1 ,u 2 plane for C=10fF to 500fF by grid method. In the range of C=10fF to 260fF the circuit was actually characterized only by three areas of attraction for stable singularities S1, S2 and S3, what the authors of [17] considered a condition for smooth memory control. However, when cross sections were made through the unstable singularities N1, N2, it turned out that at C=10fF (Fig.2) BS does not pass through the saddle point N1 (BS does not separate attractors S1 and S2), as it is for C=20fF (Fig.3) to 260fF.…”