Here are some paraphrased contemporary definitions of complex systems from people at the Santa Fe Institute.
Krakauer: "Systems that don't have a compact description because they encode long histories from their environment."
Moore: "Questions are complex if they require a lot of resources to answer. There may be no short cut to doing a laborious step-by-step simulation in real-time."
Crutchfield: "A complex system has a sophisticated internal architecture that stores and processes information."
Rundle: "A system with interactions and non-linear elements, often with power laws and/or fractal elements."
Page: "Systems capable of producing complexity have adaptive, responsive entities that are connected in a network, interdependent with each other, and end up being diverse (even if they started out as the same). Sometimes systems with these characteristics end up in an equilibrium or a predictable pattern and so don't result in complexity."
Newman: "A system of many interacting parts where the system shows emergent behavior."
Forrest: "Complex systems have many active, interacting components with non-trivial and non-linear interactions resulting in non-predictable behavior . The components are capable of learning or otherwise modifying their behavior."
Farmer: "A complex system has a lot of interacting parts with emergent phenomenon."
Bettencourt: "Complex systems tend to be made of heterogeneous parts, tend to be open-ended (evolving), and they often have circular casual chains that provide positive and negative feedback loops."
West: "Complex systems involve enormous numbers of agents interacting non-linearly producing emergent phenomenon. Complex systems are evolving and adapting and can't be described with a few simple equations."