After some mathematical noodling (whilst awaiting a replacement oscilloscope), I've come up with two bizarre expressions for the exact equilibrium position of the coupled FitzHugh-Nagumo attractor (as per previous posts), for the cases in which coupling parameter k = -1 and 0 respectively:
C3(n) is the nth Fuss-Catalan number of order 3, or ternary number [1], the first few terms being 1, 1, 3, 12, 55, 273, 1428, 7752...
Given x1, we can readily obtain y1 from (as per previous post):
Example
Using the above equations for x1, with a = 0.4, b= 0.5, c = 0.01, as per Sprott's figure 6.7, we calculate
x1 = -0.7901341941135... (k = -1 case), and
x1 = -0.8056544203709... (k = 0 case).
These agree with the values for x1 given by equations (7) and (8) in the previous post.
Reference
[1] Sequence A001764, N. J. A. Sloane, A Handbook of Integer Sequences, New York and London: Academic Press (1973). Online at https://oeis.org
C3(n) is the nth Fuss-Catalan number of order 3, or ternary number [1], the first few terms being 1, 1, 3, 12, 55, 273, 1428, 7752...
Given x1, we can readily obtain y1 from (as per previous post):
Example
Using the above equations for x1, with a = 0.4, b= 0.5, c = 0.01, as per Sprott's figure 6.7, we calculate
x1 = -0.7901341941135... (k = -1 case), and
x1 = -0.8056544203709... (k = 0 case).
These agree with the values for x1 given by equations (7) and (8) in the previous post.
Reference
[1] Sequence A001764, N. J. A. Sloane, A Handbook of Integer Sequences, New York and London: Academic Press (1973). Online at https://oeis.org
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