Dynamical systems in the world are rarely isolated but generally interact with each other and are often oscillatory.

Examples of such dynamical systems include:

• Climate
• Diurnal (day/night) rhythms
• Communications (for credit cards, radio, telephones)
• Democracy and economic growth
• Population cycles
• Nerve cells in the brain
• Diseases
• Solar cycles
• The heart-lung connection

The coupling functions that link all these systems contain detailed information about the functional mechanisms underlying their interactions and prescribe the physical rule specifying how each interaction occurs. Coupling functions focus not so much on whether there are interactions, but more on how they appear and develop.

Knowledge of such coupling function mechanisms can be used to detect, engineer, or predict certain physical effects, to solve some man-made problems and, in living systems, to reveal their state of health and to investigate changes due to disease.

The prestigious Reviews of Modern Physics has now published a review paper on coupling functions.

The authors of the review, all of whom have played an important role in the development of the field, are Dr Tomislav Stankovski (Lancaster University, UK and Ss Cyril and Methodius University, Macedonia), Dr Tiago Pereira (Imperial College London, UK and University of Sao Paulo, Brazil), Professor Peter McClintock and Professor Aneta Stefanovska (Lancaster University, UK).

Professor Stefanovska  said: “The review outlines in some detail our present theoretical understanding of coupling functions together with methods of extracting them from data. So we anticipate that our review will help to foster even wider applications in the future, and that coupling functions will be used for controlling, engineering and predicting all manner of interactions.”

The article outlines the basic concepts underlying coupling functions, followed by a rigorous theoretical description. State-of-the-art methods for analysing coupling functions are presented and compared in the light of how best to reconstruct them from measured data.

Although stemming from physics, such methods are being applied in diverse areas of science and technology, including chemistry, biology, physiology, neuroscience, social sciences, mechanics, and secure communications. This breadth of application illustrates the universality of coupling functions for studying the interaction mechanisms of coupled dynamical systems.

Professor McClintock said: “Given that interactions are all around us, we hope that our paper will serve as the prime source of knowledge on the subject for many, in their quest of revealing the underlying mechanisms of interactions.”