Correction to Frisch’s Propagation-Impulse Model: A Comprehensive Mathematical Analysis

Correction to: Foundations of Science https://doi.org/10.1007/s10699-021-09827-9

In Sect.  3.2.6., in the first paragraph after Eqs. (31) the following sentence:

“where the “cyclical components” …”

must be replaced by

“where the “trend” and the “cyclical components” …”

In Sect. 3.2.6., in the paragraph:

“Nevertheless, there is a main drawback in Zambelli’s procedure: he did not normalize the coefficients a_j, b_j and c_j. In other words, in the above expression (32) of x(t), Zambelli posed ${a}_{0}={a}_{1}={a}_{2}={a}_{3}=1$.”

The last sentence must be replaced by:

“In other words, in the above expression (32) of x(t), Zambelli posed ${a}_{1}={a}_{2}={a}_{3}=1$.”

In Sect. 3.2.6., in the paragraph after Fig. 6 the following sentence:

“Unfortunately, it does not seem that Zambelli has taken into account such normalization since in his case ${a}_{0}+{a}_{1}+{a}_{2}+{a}_{3}=4$”

must be replaced by

“Unfortunately, it does not seem that Zambelli has taken into account such normalization since in his case ${a}_{1}+{a}_{2}+{a}_{3}=3$”.

The following sentence:

“This solution x(t) has been plotted in Fig. 6 below with the following parameters: ${a}_{0}=0.01, {a}_{1}=0.1, {a}_{2}=0.2, {a}_{3}=0.699$, the sum of which is obviously equal to unity, as recommended by Frisch”.

must be replaced by:

“This solution x(t) has been plotted in Fig. 6 below with the following parameters: ${a}_{1}=1, {a}_{2}=+30, {a}_{3}=-30$, the sum of which is obviously equal to unity, as recommended by Frisch”.

So Fig. 6 may be replaced by the following one:

Fig. 6

Solution x(t) of Frisch’s system (11), i.e., of MODEL 2