This paper studies the rotation map with a controlling segment. As a parameter varies, the map exhibits superstable periodic orbits, chaos and rich bifurcation phenomena. The map is applicable to an A/D converter having efficient resolution characteristics. The converter can be realized as a circuit model based on a spiking neuron and the rate-coding. Presenting a test circuit, basic operation ...

The stability behaviour of the functional equation F (y) − F (x) = (y − x)f ( (x+ y)/2 ) is studied. It is proved that this equation is superstable i.e. if f, F satisfy ∣∣F (y) − F (x)(y − x)f((x + y)/2)∣∣ ≤ ε then f satisfies this equation (with some F ). In order to obtain this result the equation h∆hf(x) = 0 is considered and it is proved that also this equation is superstable.

Aval et al. proved in [2] that starting from a critical configuration of a chipfiring game on an undirected graph, one can never achieve a stable configuration by reverse firing any non-empty subsets of its vertices. In this paper, we generalize the result to digraphs with a global sink where reverse firing subsets of vertices is replaced with reverse firing multi-subsets of vertices. Consequen...

We study a particular bifurcation structure observed in the parameter space of a one-dimensional continuous piecewise smooth map generated by the credit cycle model in [23] where the map is de…ned over the absorbing interval via three functions, one of which is a constant. We show that the ‡at branch gives rise to superstable cycles whose periodicity regions are ordered according to a modi…ed U...

The superstability of a dynamical motion is defined with existence of a minus infinity Lyapunouv exponent, this mean that this motion is attractive. There are several methods for constructing 1-D polynomial mappings with attracting cycles or superstable cycles [1,2] based on Lagrange and Newton interpolations. Superstable phenomena in some 1-D maps embedded in circuits and systems are studied i...