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This thesis sheds some lights on the on-going discussions on modelling the economy as a complex evolving system. It introduces a complex systems approach and attempts to unfold the underlying mechanisms of dynamic instability in complex economic system. Moreover, it contributes to the ongoing discussions on early warnings for financial crises and the transmissions of the complexity based economic policy. As a complex system, economic system possesses the characteristics of complex systems. This thesis focuses on three features: critical transitions, catastrophe theory and expectations. The methodologies developed and applied include statistical time series tools and agent-based modelling.