Most of the systems that surround us are complex and many events that appear independent are often influenced by each other. A system can be a swarm of insects, a group of people, a business, a herd of animals or a collection of atoms.
Many complex systems contain a large number of interacting agents. Consider for example the outbreak of a disease. Contagious individuals usually do not act in isolation, but interact with others and pass on the disease to further individuals who themselves infect others. Understanding which fraction of the population will be diseased after a certain time or which immunization strategies are likely to be successful requires a deep understanding of the heterogeneous contact pattern and its macroscopic consequences.
Other aspects of complex systems are adopting and herding. Herding behaviour can be found in many different systems - not only in ecosystems, but also in financial markets. Understanding the emerging macro-outcomes induced by herding in terms of individual behaviour is a vital area of research. The financial crisis is one example of a macro outcome of aggregated individual behaviour. Its origins lay in the interdependent structure of the financial system that facilitates the propagation of distress and intensifies the severity of shocks.
Further research areas around complex systems consider the spread of rumours and opinions in societies. Taking the underlying network structure of a community into account aids the understanding of the latest trends and their ability to persist.
But complex systems exist also on a much smaller scale. Consider for instance regulatory mechanisms in biology such as gene expression, which cannot be understood in terms of isolated components. These processes must be understood in terms of entire systems with all its interactions.