This paper describes the development of an efficient mechanical oscillator. It is capable of combining the energetic advantages of ballistic movement with cycle adjustability and active orbital control. Pneumatic artificial McKibben muscles are used as variable springs, from which the stiffness is varied in order to induce a limit cycle.

The well-known Hilbert’s 16th problem has remained unsolved since Hilbert proposed the 23 mathematical problems at the Second International Congress of Mathematics in 1900 [Hilbert, 1902]. Recently, a modern version of the second part of the 16th problem was formulated by Smale [1998], chosen as one of the 18 challenging mathematical problems for the 21st century. To be more specific, consider ...

The second part of Hilbert’s sixteenth problem concerned with the existence and number of the limit cycles for planer polynomial differential equations of degree n. In this article after a brief review on previous studies of a particular class of Hilbert’s sixteenth problem, we will discuss the existence and the stability of limit cycles of this class in the form of fractional differential equa...

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Suppose a group G is relatively hyperbolic with respect to a collection P of its subgroups and also acts properly, cocompactly on a CAT (0) (or δ–hyperbolic) space X. The relatively hyperbolic structure provides a relative boundary ∂(G,P). The CAT (0) structure provides a different boundary at infinity ∂X. In this article, we examine the connection between these two spaces at infinity. In parti...

It is shown that the notion of balancing a state space realization about a stable, isolated equilibrium point can be generalized to systems possessing only a stable invariant regular submanifold of arbitrary dimension, for example, a stable limit cycle.

The sensitivity properties of intermittent control are analysed and the conditions for a limit cycle derived theoretically and verified by simulation. 1 ar X iv :1 70 5. 08 22 8v 1 [ cs .S Y ] 2 2 M ay 2 01 7

Unknown process parameters are identified using limit cycle data of the relay–response curves obtained from single relay feedback test on second order plus dead time (SOPDT) processes. Time domain analytical expressions of these curves are helpful in deriving conditions to estimate process parameters accurately. Identification algorithms are formulated to estimate minimal number of model parame...