The continuous Bonhoeffer–van der Pol (BVP for short) oscillator is transformed into a mapbased BVP model by using the forward Euler scheme. At first, the bifurcations and chaos of the map-based BVP model are investigated when the step size varies as a bifurcation parameter. By using the fast-slow decomposition technique, a two-parameter bifurcation diagram is obtained to give insight into the ...

Let X̃ be a connected space, X be a space, let p : X̃ −→ X be a continuous map and let (X̃, p) be a covering space of X . In the first section we give some preliminaries from covering spaces and their automorphism groups. In the second section we derive some algebraic properties of both universal and regular covering spaces (X̃, p) of X and also their automorphism groups A(X̃, p). Keywords—covering ...

The present paper points out a novel scenario for the formation of chaotic attractors in a class of models of excitable cell membranes near an Andronov-Hopf bifurcation (AHB). The mechanism underlying chaotic dynamics admits a simple and visual description in terms of the families of one-dimensional first-return maps, which are constructed using the combination of asymptotic and numerical techn...

the aim of this paper is to prove a common fixed point theorem for nonexpansive type single valued mappings which include both continuous and discontinuous mappings by relaxing the condition of continuity by weak reciprocally continuous mapping. our result is generalize and extends the corresponding result of jhade et al. [p.k. jhade, a.s. saluja and r. kushwah, coincidence and fixed points of ...

The absolutely continuous spectrum of an ergodic family of onedimensional Schrödinger operators is completely determined by the Lyapunov exponent as shown by Ishii, Kotani and Pastur. Moreover, the part of the theory developed by Kotani gives powerful tools for proving the absence of absolutely continuous spectrum, the presence of absolutely continuous spectrum, and even the presence of purely ...

Finding the MAP assignment in graphical models is a challenging task that generally requires approximations. One popular approximation approach is to use linear programming relaxations that enforce local consistency. While these are commonly used for discrete variable models, they are much less understood for models with continuous variables. Here we define local consistency relaxations of MAP ...

The input output map of linear time-continuous systems is investigated. The class of all systems for which the input output map is given by the usual integral is investigated. A complete characterization of this class of systems is given in the paper.

We characterize the entire functions which transform a weighted Banach space of holomorphic functions on the disc of type H∞ into another such space by superposition. We also show that all the superposition operators induced by such entire functions map bounded sets into bounded sets and are continuous. Superposition operators that map bounded sets into relatively compact sets are also considered.

We apply the concept of the Euler-Poincaré characteristic and the periodicity number to the index map of an isolated invariant set in order to obtain a new criterion for the existence of periodic points of a continuous map in a given set.

A map of a circle is a continuous function from the circle to itself. Such a map is transitive if there is a point with a dense orbit. For degree one transitive maps of the circle with a fixed point, we give all possible sets of periods and the best lower bounds for topological entropy in terms of the set of periods.