This paper attempts to develop an analytic tool for exploring whether dynamic processes in different complex adaptive systems share a common evolutionary mechanism over time. A nonlinear autoregressive integrated (NLARI) model is derived from a class of nonlinear systems with resilience mechanisms by using Newton’s second law to stochastic systems. Whether NLARI effectively models a class of dynamic processes in complex adaptive systems with common evolutionary mechanism depends on whether it can characterize and predict major dynamics of time series data from these systems. This study finds that a relative restoring coefficient controls bifurcation and stability of NLARI’s deterministic system. Unexpectedly, unstable oscillations may be because the relative restoring coefficient is too large or too small due to a weak resilience, while a stable fixed point and stable period-2 cycle only occur in an approximate value of the relative restoring coefficient.

time series model, nonlinear dynamics, exact solutions of difference equation, stability, Lyapunov exponents.