Applying attractor reconstruction techniques and other chaotic measurements, it is shown that the long-term dynamics of a vertical, underactuated, two-degrees-of-freedom robot called Pendubot may exhibit complex dynamics including chaotic behavior. These techniques use only the measurement of some available variable of the system, and the resulting reconstruction allows us to identify unstable ...

It is possible that self-excited vibrations in turbine blades synchronize due to elastic coupling through the shaft. In this context, the synchronization of four coupled van der Pol oscillators is studied here. For quasilinear oscillations, a stability condition is derived from an analysis based on linearizing the original equation around an unperturbed limit cycle and transforming it into Hill...

Grid cells in the rodent medial entorhinal cortex exhibit remarkably regular spatial firing patterns that tessellate all environments visited by the animal. Two theoretical mechanisms that could generate this spatially periodic activity pattern have been proposed: oscillatory interference and continuous attractor dynamics. Although a variety of evidence has been cited in support of each, some a...

Applying attractor reconstruction techniques and other chaotic measurements, it is shown that the long-term dynamics of a vertical, underactuated, two-degrees-of-freedom robot called Pendubot may exhibit complex dynamics including chaotic behavior. These techniques use only the measurement of some available variable of the system, and the resulting reconstruction allows us to identify unstable ...

In this paper, the averaging principle for quasi-geostrophic motions with rapidly oscillating forcing is proved, both on nite but large time intervals and on the entire time axis. This includes comparison estimate, stability estimate, and convergence result between quasi-geostrophic motions and its averaged motions. Furthermore, the existence of almost periodic quasi-geostrophic motions and att...

In this paper, the averaging principle for quasi-geostrophic motions with rapidly oscillating forcing is proved, both on nite but large time intervals and on the entire time axis. This includes comparison estimate, stability estimate, and convergence result between quasi-geostrophic motions and its averaged motions. Furthermore, the existence of almost periodic quasi-geostrophic motions and att...

We show that for periodic non-autonomous discrete dynamical systems, even when a common fixed point for each of the autonomous associated dynamical systems is repeller, this fixed point can became a local attractor for the whole system, giving rise to a Parrondo’s dynamic type paradox. Mathematics Subject Classification 2010: 37C05, 37C25, 37C75, 39A30.

Herein I define the global attractor for the semidynamical system (H, {S(t)}t≥0), where H is a Hilbert space and S(t) is a semigroup. In particular, I will consider the semigroup S(t) which acts on a relevant function space by S(t)u0 = u(t; u0), where u(t; u0) is the solution of a given partial differential equation at time t with initial condition u(0) = u0. By imposing regularity properties o...

Heteroclinic cycles may occur as structurally stable asymptotically stable attractors if there are invariant subspaces or symmetries of a dynamical system. Even for cycles between equilibria, it may be difficult to obtain results on the generic behaviour of trajectories converging to the cycle. For more complicated cycles between chaotic sets, the nontrivial dynamics of the ‘nodes’ can interact...

The generalized spectral decomposition of the Frobenius-Perron operator of the tent map with varying height is determined at the band-splitting points. The decomposition includes both decay onto the attracting set and the approach to the asymptotically periodic state on the attractor. Explicit compact expressions for the polynomial eigenstates are obtained using algebraic techniques. (c) 1998 A...