The catastrophe theory and the deterministic chaos constitute basic elements of the science of complexity. Elementary catastrophes were the first remarkable form of nonlinear, topological complexity that were seriously studied in economics. The deterministic chaos and other types of complexity succeed the catastrophes theory. In general, chaos means seemingly random behavior of a deterministic system, which stems from high sensitivity to initial condition. The nonlinear dynamical systems theory, which unites various manifestations of complexity into one integrated system, is contrary to assumptions that markets and economies spontaneously strive for the state of equilibrium. Just the opposite, their complexity seems to grow due to the influence of classic economic laws. In my paper, I indicate that with time model economic systems strive for the state we call the edge of chaos. I consider three cases. The first one concerns the cobweb theorem and indicates that price expectations shape up in such a way that it makes the market more complex. Next, I consider the Cournot-Puu duopoly model in which striving for the edge of chaos stems from profit maximization by entrepreneurs. The third case concerns an economy based on a two-stage accelerator, where the economic cycle takes up a form of chaotic hysteresis. The evolution of systems at the edge of chaos can be sudden, which makes it necessary to consider it in terms of elementary catastrophes.

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