A control approach to complexity : from molecular vibrational dynamics to competition games on networks

Abstract

The ever-increasing understanding of the inherent laws underpinning the reality around us is a continuous quest that goes back to centuries of scientific advances. The foundational physical principles associated to many real systems were discovered more than a century ago, and at this point our comprehension of a wide range of phenomena around us has reached a high level of maturity. This evolution in knowledge has eventually allowed humankind to design mechanisms, strategies, devices and algorithms aiming to dominate the associated dynamics in numerous applications and technologies. Many of these accomplishments are related to control theory, which is used in a wide range of scenarios in industry, automation, aerospace, robotics, etc. It should be noted that these fields have a heavy reliance on the knowledge of physics such as fluid dynamics, classical and quantum mechanics, electromagnetism, etc, all these disciplines being by now strongly developed and understood by the scientific community.On the other hand, a step beyond has been achieved in recent decades in many areas whose complexity prevented until recently a proper explanation of their inherent behaviour. This is the case of many fields which are now being tackled from a different point of view, such as stock markets, public opinion trends, gene networks, illness propagation, neuroscience, etc. Reality is inherently complex, and in fact ours is meant to be the century of complexity, according to distinguished minds such as S. Hawking, H. Pagels or E. Wilson [Wil98]. The comprehension of complex systems will be one of the subjects of study and research addressed by many different institutions, academia, private companies, etc.The so called complexity theory encompasses many different disciplines such as complex networks, emergency, chaos theory, etc. The structural and dynamical phenomena observed in many circumstances are better understood with the introduction of these new tools of analysis. As in the case of more classical phenomena listed above, in the case of complex systems it is natural that science will make every effort to acquire tools for the control of such iii iv ABSTRACT complexity to the benefit of particular entities or for the common wealth in modern societies. Control of complex systems is therefore an area already subject to an intensive research activity.Following this rationale, this thesis addresses the topic of complex systems from the perspective of control theory. One of the studied problems is the subject of control of molecular vibrational dynamics, which is very relevant in chemistry due to the applications in chemical processes, etc. The research conducted here provides an important insight in terms of control of those dynamics by means of an external time-varying magnetic field. In particular, a laserperturbed HCN molecular system is studied, in terms of transitions between chaotic and regular dynamics, molecular dissociation, and the relation of both of them with the frequency of the excitation laser. It has been observed ...