On asymptotic stability of discrete-time non-autonomous delayed Hopfield neural networks

AbstractIn this paper, we obtain some sufficient conditions for determining the asymptotic stability of discrete-time non-autonomous delayed Hopfield neural networks by utilizing the Lyapunov functional method. An example is given to show the validity of the results

Self-synchronization theory of a nonlinear vibration system driven by two exciters. Part 2: Numeric analysis and experimental verification

A single mass nonlinear vibration machine driven by two counter-rotating motors was taken as a research object. Based on the mechanic-electric coupling dynamic equation of the vibration machine and the electromagnetic torque model of motor, the simulation model was established. By using the actual parameters of the vibration machine, the numerical simulation of a single-mass nonlinear vibration system under three typical working states was performed. When two motors were working under the ideal state, or when the overlap angle of two eccentric blocks were different, or when the supply frequency of one motor was changed, the two motors can achieve steadily synchronous motion if parameters of the vibration system are in specific range. Finally, the self-synchronization experiment was carried out under the three working states. A comparison of experimental results with simulation results shows that the numerical simulation is accurate

Peratic Phase Transition by Bulk-to-Surface Response

The study of dynamical phase transitions has been attracting considerable research efforts in the last decade. One theme of present interest is to search for exotic scenarios beyond the framework of equilibrium phase transitions. Here, we establish a duality between many-body dynamics and static Hamiltonian ground states for both classical and quantum systems. We construct frustration free Hamiltonians whose ground state phase transitions have rigorous duality to chaotic transitions in dynamical systems. By this duality, we show the corresponding ground state phase transitions are characterized by bulk-to-surface response, which are then dubbed "peratic" meaning defined by response to the boundary. For the classical system, we show how the time-like dimension emerges in the static ground states. For the quantum system, the ground state is a superposition of geometrical lines on a two dimensional array, which encode the dynamical Floquet evolution history of one dimensional disordered spin chains. Our prediction of peratic phase transition has direct consequences in quantum simulation platforms such as Rydberg atoms and superconducting qubits, as well as anisotropic spin glass materials. The discovery would shed light on the unification of dynamical phase transitions with equilibrium systems.Comment: 6+8 pages; 3+4 figure

The Modeling of Interval-Valued Time Series Using Possibility Measure-Based Encoding-Decoding Mechanism

Interval-valued time series (ITS) is a collection of interval-valued data whose entires are ordered by time. The modeling of ITS is an ongoing issue pursued by many researchers. There are diverse ITS models showing better performance. This paper proposes a new ITS model using possibility measure-based encoding-decoding mechanism involved in fuzzy theory. The proposed model consists of four modules, say, linguistic variable generation module, encoding module, inference module and decoding module. The linguistic variable generation module can provide a series of linguistic variables expressed in fuzzy sets used to described dynamic characteristics of ITS. The encoding module encodes ITS into some embedding vectors with semantics with the aid of possibility measure and linguistic variables formed by linguistic variable generation module. The inference module uses artificial neural network to capture relationship implied in those embedding vectors with semantic. The decoding module decodes for the outputs of the inference module to produce the output of linguistic and interval formats by using the possibility measure-based encoding-decoding mechanism. In comparison with existing ITS models, the proposed model can not only produce the output of linguistic format, but also exhibit better numeric performance