Classical economic theories prescribe specialization of countries industrial production. In- spection of the country databases of exported products shows that this is not the case: suc- cessful countries are extremely diversified, in analogy with biosystems evolving in a com- petitive dynamical environment. The challenge is assessing quantitatively the non-monetary competitive advantage of diversification which represents the hidden potential for develop- ment and growth. Here we develop a new statistical approach based on coupled non-linear maps, whose fixed point defines a new metrics for the countries Fitness and products Com- plexity. We show that a non-linear iteration is necessary to bound the complexity of products by the fitness of the less competitive countries exporting them. We show that, given the paradigm of economic complexity, the correct and simplest approach to measure the com- petitiveness of countries is the one presented in this work. Furthermore our metrics appears to be economically well-grounded.