Complex systems appear in diverse disciplines such as physics, economics, banking and finance, ecosystems, molecular biology, neuroscience, psychology and sociology.
Typically these systems are comprised of a large number of interconnected components which interact collectively, leading to emergent behaviour, such as self-organisation, which is not apparent from the properties of the underlying components.
As an example of complex systems in financial markets, there is considerable interest in developing a mathematical understanding of the dynamics of the order book, which records all bids to buy and sell on the stock market at the milli- to micro-second level.
Examples in physics are models in statistical mechanics, many body theory, dynamical systems, and in particular networked dynamical models in which a large number of nodes interact nonlinearly across a network which has various connectivity properties. Each node can behave classically, such as a harmonic oscillator or a chaotic system, or even as a quantum system.
For certain models with suitable nonlinear interactions all nodes of the complex system can oscillate in synchrony to a common frequency, a remarkable phenomenon which has been extensively studied over the past decade. Dynamical complex systems are generally investigated by means of numerical computations, particularly for nontrivial network topologies, although there is scope for advanced theoretical and mathematical analysis.
Theoretical physics research activities cover a broad range of topics and are primarily carried out under the umbrella of the ARC Centre for the Subatomic Structure of Matter (CSSM).