Chapter 41
Catastrophe
The choice of the name, catastrophe theory, is unfortunate as it
denotes abnormal nasty events. What we have come to realize is
that such events are normal and necessary for the continued
smooth functioning of many systems.
(E.D. Schneider and J.J. Kay. 1994. Complexity and Thermodynamics, Futures, Vol. 26, p. 641)
41.1 Catastrophe Model
If a large number of real systems exhibit dynamics that bear the potential for chaos,
why do we not see more chaos in real-world processes? Fortunately, the domains
over which stability of the system occurs can be relatively large. But once in a
while, systems may move “towards the edge of stability” and little nudges to the
system may move it from stability to instability—that is, into a catastrophe.
Subsequently, reorganization of system components may occur to bring the system
back into a stable domain—a kind of evolutionary process. This stable domain,
however, may not be the same as the one prior to the disturbance.
The system undergoes a catastrophic event in the sense that it is moved from an
initial state of stability through a dramatic phase of reorganization and back to
some degree of stability. Examples for such catastrophic events include landslides,
avalanches, earthquakes, and pest outbreaks in ecosystems. In each case, small
changes in the system occur that individually may not be critical to the system’s
behavior. Collectively, however, they lead to the evolution of the system towards
a critical state. This is apparent, for example, in the case of avalanches.
A save-disabled version of STELLA and the computer models of this book are available at
www.iseesystems.com/modelingdynamicbiologicalsystems.
B. Hannon and M. Ruth, Modeling Dynamic Biological Systems,
Modeling Dynamic Systems, DOI 10.1007/978-3-319-05615-9_41,
© Springer International Publishing Switzerland 2014
377
Catastrophe
The choice of the name, catastrophe theory, is unfortunate as it
denotes abnormal nasty events. What we have come to realize is
that such events are normal and necessary for the continued
smooth functioning of many systems.
(E.D. Schneider and J.J. Kay. 1994. Complexity and Thermodynamics, Futures, Vol. 26, p. 641)
41.1 Catastrophe Model
If a large number of real systems exhibit dynamics that bear the potential for chaos,
why do we not see more chaos in real-world processes? Fortunately, the domains
over which stability of the system occurs can be relatively large. But once in a
while, systems may move “towards the edge of stability” and little nudges to the
system may move it from stability to instability—that is, into a catastrophe.
Subsequently, reorganization of system components may occur to bring the system
back into a stable domain—a kind of evolutionary process. This stable domain,
however, may not be the same as the one prior to the disturbance.
The system undergoes a catastrophic event in the sense that it is moved from an
initial state of stability through a dramatic phase of reorganization and back to
some degree of stability. Examples for such catastrophic events include landslides,
avalanches, earthquakes, and pest outbreaks in ecosystems. In each case, small
changes in the system occur that individually may not be critical to the system’s
behavior. Collectively, however, they lead to the evolution of the system towards
a critical state. This is apparent, for example, in the case of avalanches.
A save-disabled version of STELLA and the computer models of this book are available at
www.iseesystems.com/modelingdynamicbiologicalsystems.
B. Hannon and M. Ruth, Modeling Dynamic Biological Systems,
Modeling Dynamic Systems, DOI 10.1007/978-3-319-05615-9_41,
© Springer International Publishing Switzerland 2014
377