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Chaos in a non-autonomous nonlinear system describing asymmetric water wheels. (arXiv:1710.02721v1 [math.DS])
来源于:arXiv
We use physical principles to derive a water wheel model under the assumption
of an asymmetric water wheel for which the water inflow rate is in general
unsteady (modeled by an arbitrary function of time). Our model allows one to
recover the asymmetric water wheel with steady flow rate, as well as the
symmetric water wheel, as special cases. Under physically reasonable
assumptions we then reduce the underlying model into a non-autonomous nonlinear
system. In order to determine parameter regimes giving chaotic dynamics in this
non-autonomous nonlinear system, we consider an application of competitive
modes analysis. In order to apply this method to a non-autonomous system, we
are required to generalize the competitive modes analysis so that it is
applicable to non-autonomous systems. The non-autonomous nonlinear water wheel
model is shown to satisfy competitive modes conditions for chaos in certain
parameter regimes, and we employ the obtained parameter regimes to construct
the chaotic 查看全文>>