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This paper introduces an average contraction analysis for nonlinear switched systems and applies it to investigating the synchronization of complex networks of coupled systems with switching topology. For a general nonlinear system with a time-dependent switching law, a basic convergence result is presented according to average contraction analysis, and a special case where trajectories of a distributed switched system converge to a linear subspace is then investigated. Synchronization is viewed as the special case with all trajectories approaching the synchronization manifold, and is thus studied for complex networks of coupled oscillators with switching topology. It is shown that the synchronization of a complex switched network can be evaluated by the dynamics of an isolated node, the coupling strength and the time average of the smallest eigenvalue associated with the Laplacians of switching topology and the coupling fashion. Finally, numerical simulations illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

We introduce a general random pseudofractal network model by assigning fitness to each edge. In this model, continuous growth and attachment, determined by their fitness of already existing edges, are the two ingredients. We obtain the analytical results that our model exhibits a power-law degree distribution with exponent g = 2 + m(1 + am)[?]1, where m and a are tunable parameters. We also show that a general random pseudofractal network has a large clustering coefficient and a small average distance leading to a small-world effect. These theoretical results agree well with numerical simulations. [ABSTRACT FROM AUTHOR]

Hypergraph states as real equally weighted pure states are important resources for quantum codes of non-local stabilizers. Using local Pauli equivalence and permutational symmetry, we reduce the 32 768 four-qubit real equally weighted pure states to 28 locally inequivalent hypergraph states and several graph states. The calculation of geometric entanglement supplemented with entanglement entropy confirms that further reduction is impossible for true hypergraph states. [ABSTRACT FROM AUTHOR]

A systematic analysis is performed for quantum phase transitions in a bond-alternative one-dimensional Ising model with a Dzyaloshinskii-Moriya (DM) interaction by using the fidelity of ground state wavefunctions based on the infinite matrix product states algorithm. For an antiferromagnetic phase, the fidelity per lattice site exhibits a bifurcation, which shows spontaneous symmetry breaking in the system. A critical DM interaction is inversely proportional to an alternating exchange coupling strength for a quantum phase transition. Further, a finite-entanglement scaling of von Neumann entropy with respect to truncation dimensions gives a central charge c [?] 0.5 at the critical point. [ABSTRACT FROM AUTHOR]

In this paper we investigate a variable-coefficient Korteweg-de Vries (vcKdV) model in arterial mechanics. A new Lax pair of the vcKdV model is constructed, based on which the Backlund transformation, solitonic and some other solutions of the vcKdV model are obtained. With symbolic computation, the influence of the variable coefficients on solitonic propagation is investigated based on the solitonic solution, which has the following three aspects: (i) the coefficient of the nonlinear term affects the solitonic amplitude; (ii) the coefficient of the dispersive term controls the solitonic velocity and propagation trace; (iii) the coefficient of the dissipative term acts on both the solitonic amplitude and the velocity. We also analyze the variations of velocity and pressure of blood flow along the scaled axial coordinate after the static deformation in the vicinity of stenosis. [ABSTRACT FROM AUTHOR]

This paper considers the problem of controlling a complex dynamical network by means of pinning. We point out that the synchronization criterion given in the form of matrix eigenvalues can be equivalent to a linear matrix inequality criterion. We further investigate network synchronization via pinning and prove several linear matrix inequality theorems. In particular, we theoretically provide two typical pinning strategies based on whether the graph which is made up of unpinned nodes and edges between them is irreducible or not. Numerical simulations including k-regular networks, star-shaped networks and BA scale-free networks, are shown for illustration and verification. [ABSTRACT FROM AUTHOR]