Diverse systems exhibit remarkably similar, sometimes even universal behavior. Studies solid, fluid, granular, low-temperature gas, chemical, and biological systems in aboratory experiments, numerical simulations, and theoretical analyses. Problems currently being examined include instabilities at fluid interfaces, dynamics of fluidized beds, spatial patterns and shock waves in granular flows, pattern formation in chemical reaction-diffusion systems, crack propagation in crystalline and amorphous materials, quantum chaos with ultra-cold atoms, nonlinear dynamics of bose condensates, general methods of laser cooling, viscoelasticity of actin networks, elastic properties of normal and pathological biological cells, and 'enhancement of neuronal growth'.

Nonlinear equations of motion can be solved only in rare cases. For that reason, physicists tried to build their theories on linear differential equations because they are easier to solve. And indeed, the most succesful theories (like electrodynamics and quantum mechanics) are based on linear differential equations. Other even older theories dealing with physical phenomenon closer to everday experience, like fluid dynamics, were less successful because their dynamics is nonlinear.

Yet, the advent of computers in the last decades made it possible to tackle unsolvable nonlinear problems. This possibility led to a completely different view onto dynamical systems and in association with it to a new language about dynamical systems.