Two dynamical systems are topologically equivalent when their phase-portraits can be morphed into each other by a homeomorphic coordinate transformation on the state space. The induced equivalence classes capture qualitative properties such as stability or oscillatory nature of trajectories, for example. In this paper we develop method to learn topological class an unknown stable system from si...

In this note, we derive the lower bound on the sum for Wiener index of bipartite graph and its bipartite complement, as well as the lower and upper bounds on this sum for the Randić index and Zagreb indices. We also discuss the quality of these bounds.

Each topological group G admits a unique universal minimal dynamical system (M(G), G). When G is a non-compact locally compact group the phase space M(G) of this universal system is nonmetrizable. There are however topological groups for which M(G) is the trivial one point system (extremely amenable groups), as well as topological groups G for which M(G) is a metrizable space and for which ther...

The relationship of topological insulators and superconductors and the field of nonlinear dynamics is widely unexplored. To address this subject, we adopt the linear coupling geometry of the Su-Schrieffer-Heeger model, a paradigmatic example for a topological insulator, and render it nonlinearly in the context of superconducting circuits. As a consequence, the system exhibits topologically enfo...

Topological insulators are a new class of materials that exhibit robust and scatter-free transport along their edges - independently of the fine details of the system and of the edge - due to topological protection. To classify the topological character of two-dimensional systems without additional symmetries, one commonly uses Chern numbers, as their sum computed from all bands below a specifi...

The general, differential-equation-independent definition of a continuous-time controlled dynamical system as well as of the state space transformation and static state feedback are introduced. This approach makes it possible to consider transformations that are not smooth and introduce the so-called topological equivalence of controlled dynamical sys­ tems. It is shown that this approach gener...

We investigate the effect of topological disorder on a system of forced threshold elements, where each element is arranged on top of complex heterogeneous networks. Numerical results indicate that the response of the system to a weak signal can be amplified at an intermediate level of topological disorder, thus indicating the occurrence of topological-disorder-induced resonance. Using mean fiel...

in this paper, the notion of fuzzy semicompactness degrees isintroduced in $l$-fuzzy topological spaces by means of theimplication operation of $l$. characterizations of fuzzysemicompactness degrees in $l$-fuzzy topological spaces  areobtained, and some properties of fuzzy semicompactness degrees areresearched.

Magnetic doping is expected to open a band gap at the Dirac point of topological insulators by breaking time-reversal symmetry and to enable novel topological phases. Epitaxial (Bi(1-x)Mn(x))2Se3 is a prototypical magnetic topological insulator with a pronounced surface band gap of ∼100 meV. We show that this gap is neither due to ferromagnetic order in the bulk or at the surface nor to the loc...