Identification of chaotic systems with hidden variables (modified Bock’s algorithm)

Analytic reconstruction of some dynamical systems

“…where A 1 = −254, A 2 = −10, A 3 = −10, A 5 = −143. Solutions of system (18) and its phase portraits are shown in Fig. 4.…”

“…Since relations (19) involve 9 coefficients, when considering candidate systems [37] to choose a unique real OS from, it is necessary to check relations (19) for possible combinations of 6 coefficients from 9 as to satisfy conditions in Proposition 2. To this end, it is sufficient to alternatively set 3 out of 9 coefficients to zero and check whether the structure of the SS is that of (18). Such transformations are carried out in Appendix C. As the result we get the OS's S 1 -S 8 , see Table 2.…”

“…Namely, if the conditions of the experiment change at least one of the coefficients of the OS, then the observable y 1 (t) ≡ x 2 (t) will change. The reconstruction in form (18) obtained from this observable will have the value of at least one of the coefficients A 1 , . .…”

“…. , u m2 ) we get a new time series y 12 (t) and new reconstruction of type (18) with new coefficients A 12 , A 22 , A 32 , A 52 . 3.…”

“…When constructing Table 5, various cases that may occur when external effects are applied to the OS were considered. For example, if the coefficient A 1 changes when using reconstruction (18) from the observable in system S 2 , then, according to Table 4, this can occur if one of the coefficients of the OS changes, namely the coefficient c 2 . If system S 1 is considered, a change of A 1 can only occur if b 1 or c 2 change in the OS.…”