On q-dynamic equations modelling and complexity

In this work, q   and q∗q∗ (a dual to the q-derivative)-dynamic equations are introduced. It is shown that q   and q∗q∗-derivatives measure the effects of compression and amplified transport memories, respectively with relevance to dynamical systems. Complexity in q-dynamic equations is obviously viewed in the linearized model. Abrupt high oscillations in solutions of the dynamic equations and “pattern formation” do occur. Pattern formation is induced by undeterministic memory compression and amplified memory transport associated with q   and q∗q∗-difference operators, respectively.