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"Application of Bifurcation Analysis for the Detection of Invariants in Large Dimensional Complex Systems"

Elena Surovyatkina (Space Research Institute of Russian Academy of Sciences)

Abstract:

The difficulties in the investigation of large dimensional complex systems and the control of the complex processes are well known. The traditional application of statistical methods to complex systems solves the problems of analysis of the most typical and mass processes and its dynamics in time. However, the statistical analysis does not allow us to couple up the description of different semantic levels in a single whole so the decomposition problem is unsolved yet.

Complex systems are extremely labile to external conditions and assume a broad spectrum of states and consequences which are some times not equiprobable. Moreover, in complex systems the objects of even one class are strongly variable. It is known that control over complex systems is possible only when stable laws are shown to be invariants of lability and variability. Recognizing these laws is possible only through modeling experiments.

I will present a method for detection of the lability and variability invariants based on a bifurcation analysis by example of the electrical conduction system of a single cardiac cell described by the large dimensional complex model. I will show that the result obtained of the multistability mechanism is invariant by both the lability of the control process and also the variability of states of the objects of one class.

Finally, I will point out that the suggested approach is not restricted to a certain application but it is applicable to complex system analysis of different nature, for example, in geophysics for invariant detection in complex systems, and also in engineering for the elaboration of the control system of the complex objects.