Dynamic Bifurcations in Non-Stationary Systems: Transitions with an Unpredictable Outcome

M. S. Soliman
1995 Proceedings of the Royal Society A  
D y n a m ic b if u r c a tio n s in n o n -s ta tio n a r y s y s te m s : tr a n s itio n s w ith a n u n p r e d ic ta b le o u tc o m e In nonlinear non-stationary systems, dynamic bifurcations result in a transition to a qualitatively new state. In this paper we examine how the dynamics of transition of such systems may be assessed using the concept of transient basins of attraction. We delineate the phenomenon of indeterminate dynamic bifurcations, where it is shown that the response,
more » ... t the response, after the system passes through critical parameter values, may be extremely sensitive to the choice of initial conditions or parameter states. This new form of unpredictability in systems whose parameters vary with time, is clearly an im portant concept to be assimilated in the theory of non-stationary dynamics.
doi:10.1098/rspa.1995.0137 fatcat:hqzioc76h5gozenbaowhggpr4m