Florida's election system seems to have run aground somewhere along its shoreline (front page, Nov. 20), but, in fairness, the same potential chaos exists in every state election.
Hence, the FOIM system is stable, and chaos exists in the incommensurate system.
However, regions of bounded fluctuations that continue forever, including both periodicity and chaos, exist in the parametrical plane outside the asymptotically stable region.
It is found that chaos exists in the fractional-order system (16) when (alpha > 0.94) with the initial condition ((x_0,y_0,z_0) = (0.7,0.1,0)).
Although whether the energy spectra are discrete or not is not crucial to quantum chaology, whether a quantum system is isolated or not has been argued to be potentially important to whether chaos exists in the quantum realm.
It has been proved that chaos exists in the permanent-magnet synchronous motor (PMSM) system when its parameters satisfy some condition, and it would degrade the efficiency of the PMSM system dramatically.
Furthermore, it is shown by using the invariance of the modal subspaces that this chaos exists for the full beam equation: i.e., the partial differential equation of motion.
Therefore, from the Lyapunov exponents and bifurcation diagrams in these figures we conclude that chaos exists in the fractional-order system (6) when selecting a certain range of parameters.
Chaos in a fractional order modified van der Pol system is studied by [9], where chaos exists in the fractional order system with the order both less than and higher than the number of the states of the integer order generalized van der Pol system.
