On the Dynamics of the Nonlinear Rational Difference Equation x_{n+1}=Ax_{n}+Bx_{n-a}+((ax_{n-a}+bx_{n-k})/(cx_{n-a}+dx_{n-k}))

Abstract

Both the optimization and equilibrium principles turn out to be more akin to common sense than to science. They have been postulated as describing markets, but lack the required empirical underpinning. Optimization is not a magic cure. In order to particularly circumvent some of the technical obstacles for a control problem , it turns out to be practically effective to reduce the system dynamics to a system of ordinary differential equations of considerably higher dimension, Such an approach might replace a theoretical difficulty by a greatly increased computational problem.