Functional-differential and discrete equations of regulatorics (Q2772165)

Differential-difference, functional and discrete equations of autonomous systems' regulation mechanisms are considered. One of them has the form NEWLINE\[NEWLINE\alpha^{-1}dX(t)/dt=aX^n(t-1)\exp(n(1-X(t-1)))-X(t),NEWLINE\]NEWLINE where \(\alpha, a>0,\;n>1\). Simplification leads to the functional equation NEWLINE\[NEWLINEX(\tau)=aX^n(\tau-1)\exp(-X(\tau-1))NEWLINE\]NEWLINE and then to the discrete equation \(X_{k+1}=aX_k^n\exp(-X_k)\). Qualitative analytic results of equations of associative, inter-integrated and self-integrated regulation systems are given.