TOWARD CULTURAL ONCOLOGY: THE EVOLUTIONARY INFORMATION DYNAMICS OF CANCER

dKR/dR = u1dlog(f)/dR + u2/R

v₂

dJR/dR = vjd log(f )/dR + r Jr.

(10)

The ui, vi, i = 1, 2 are functions of KR, JR, but not explicitly of R itself.

We expand these equations about the critical value KR = KC and about
J_R = 0, obtaining

dKR/dR = (KR - KC)ydlog(f)/dR + (KR - KC)z/R
dJ_R/dR = wJ_Rd log(f)/dR + xJ_R/R.

(11)

The terms y = du₁/dK_R|_KR=KC, z = du₂/dK_R|_KR=KC, w = v₁(K_C, 0), x =
v2 (KC, 0) are constants.

Solving the first of these equations gives

KR=KC+(K-KC)R^zf(R)^y,

(12)

again remembering that K₁ = K, J₁ = J, f (1) = 1.

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