textbook-theory · English
Difference Equations to Differential Equations — Section 1.5: Nonlinear Difference Equations
Section 1.5 of Dan Sloughter's open calculus textbook introduces nonlinear difference equations through the discrete logistic (inhibited growth) model, contrasting it with the linear uninhibited growth model. The section analyzes convergence behavior as the growth-rate parameter varies: convergence to the carrying capacity M for 0 < alpha <= 2, period-2 and period-4 limiting cycles for larger alpha values, and chaotic behavior near alpha = 2.95. Eight exercises reinforce the concepts using population-ecology scenarios and discrete dynamical systems.
nonlinear difference equationsdiscrete logistic equationpopulation dynamicschaos and limiting cycles