The generation of technological knowledge is paramount to our present development. Economic science concentrates on representing the functions of production applied to all sectors, e.g., the well known Cobb-Douglas model, associated with parameters such as capital and labor. Based on the paradigm, demonstrated in another paper, that the production of technological knowledge is governed by the same Cobb-Douglas type model, by the means of research and the intelligence level replacing capital, respectively labor, we are exploring the basic behavior of present days economies that are producing technological knowledge, along with the 'usual' industrial production. Considering the intercorrelations of technology and industrial production we determine a basic behavior that turns out to be a 'Henon attractor', well known as one of the first analyzed systems that present chaotic behavior confined to strange attractors. The behavior inside the basin of the attractor's dynamic shows some interesting features such as the fact that too little effort in technological knowledge production is associated to low industrial production, while too much resource allocation to technological production is also reaching an area of low industrial production. This effect clearly shows that too little allocation of resources to research is equivalent to a disproportionate allocation of resources to research, namely that both hamper the industrial production. Moreover, there is an area of large industrial production that corresponds to a certain rate of technology production that, in some way, optimizes development. Measures are introduced for the gain of technological knowledge and the information of technological sequences that are based on the underlying multi-valued logic of the technological research and on nonlinear thermodynamic considerations. We have witnessed in the last decades several cases of economies, e.g., Ireland and Finland, in Europe, the Asian tigers and China in Asia, which had had a moment in their history when research (both means and intelligence) was a main priority. Luckily, the globalization acted as a stabilizer that kept them close to the optimum of 'As High As Reasonably Acceptable' technological production. By contrast to ALARA (as low as reasonably acceptable) principle, that applies in risk analysis, here we may introduce the AHARA principle resulting from the nonlinear behavior of technological production vs. industrial production.
