The Ramifications of Meddling with Systems Governed by Self-organized Critical Dynamics

Complex natural, well as man-made, systems often exhibit characteristics similar to those seen in self-organized critical (SOC) systems. The concept of self-organized criticality brings together ideas of self-organization of nonlinear dynamical systems with the often-observed near critical behavior of many natural phenomena. These phenomena exhibit self-similarities over extended ranges of spatial and temporal scales. In those systems, scale lengths may be described by fractal geometry and time scales that lead to 1/f-like power spectra. Natural applications include modeling the motion of tectonics plates, forest fires, magnetospheric dynamics, spin glass systems, and turbulent transport. In man-made systems, applications have included traffic dynamics, power and communications networks, and financial markets among many others. Simple cellular automata models such as the running sandpile model have been very useful in reproducing the complexity and characteristics of these systems. One characteristic property of the SOC systems is that they relax through what we call events. These events can happen over all scales of the system. Examples of these events are: earthquakes in the case of plate tectonic; fires in forest evolution extinction in the co evolution of biological species; and blackouts in power transmission systems. In a time-averaged sense, these systems are subcritical (that is, they lie in an average state that should not trigger any events) and the relaxation events happen intermittently. The time spent in a subcritical state relative to the time of the events varies from one system to another. For instance, the chance of finding a forest on fire is very low with the frequency of fires being on the order of one fire every few years and with many of these fires small and inconsequential. Very large fires happen over time periods of decades or even centuries. However, because of their consequences, these large but infrequent events are the important ones to understand, control and minimize. The main thrust of this research is to understand how and when global events occur in such systems when we apply mitigation techniques and how this impacts risk assessment. As sample systems we investigate both forest fire models and electrical power transmission network models, though the results are probably applicable to a wide variety of systems. It is found, perhaps counter intuitively, that apparently sensible attempts to mitigate failures in such complex systems can have adverse effects and therefore must be approached with care. The success of mitigation efforts in SOC systems is strongly influenced by the dynamics of the system. Unless the mitigation efforts alter the self-organization forces driving the system, the system will in general be pushed toward criticality. To alter those forces with mitigation efforts may be quite difficult because the forces are an intrinsic part of the system. Moreover, in many cases, efforts to mitigate small disruptions will increase the frequency of large disruptions. This occurs because the large and small disruptions are not independent but are strongly coupled by the dynamics. Before discussing this in the more complicated case of power systems, we will illustrate this phenomenon with a forest fire model.