Frequency domain identification of non-integer order dynamical systems

Two new methods, the generalized Levy method and the weighted iteration method, are presented for identification of non-integer order systems. The first method generalizes the Levy identification method from the integer order systems to the non-integer order systems. Then, the weighted iteration method is presented to overcome the shortcomings of the first method. Results show that the proposed methods have better performance compared with the integer order identification method. For the non-integer order systems, the proposed methods have the better fitting for the system frequency response. For the integer order system, if commensurate order scanning is applied, the proposed methods can also achieve the best integer order model which fits the system frequency response. At the same time, the proposed algorithms are more stable.

Observer-based Variable Universe Adaptive Fuzzy Controller Without Additional Dynamic Order

A high-precision fuzzy controller, based on a state observer, is developed for a class of nonlinear single-input-single-output(SISO) systems with system uncertainties and external disturbances. The state observer is introduced to resolve the problem of the unavailability of state variables. Assisted by the observer, a variable universe fuzzy system is designed to approximate the ideal control law. Being auxiliary components, a robust control term and a state feedback control term are designed to suppress the influence of the lumped uncertainties and remove the observation error, respectively. Different from the existing results, no additional dynamic order is required for the control design. All the adaptive laws and the control law are built based on the Lyapunov synthesis approach, and the signals involved in the closed-loop system are guaranteed to be uniformly ultimately bounded. Simulation results performed on Duffing forced oscillation demonstrate the advantages of the proposed control scheme.

Dynamic ordering transitions in charged solid

The phenomenon of group motion is common in nature,ranging from the schools of fish,birds and insects,to avalanches,landslides and sand drift.If we treat objects as collectively moving particles,such phenomena can be studied from a physical point of view,and the research on many-body systems has proved that marvelous effects can arise from the simplest individuals.The motion of numerous individuals presents different dynamic phases related to the ordering of the system.However,it is usually difficult to study the dynamic ordering and its transitions through experiments.Electron bubble states formed in a two-dimensional electron gas,as a type of electron solids,can be driven by an external electric field and provide a platform to study the dynamic collective behaviors.Here,we demonstrate that the noise spectrum is a powerful method to investigate the dynamics of bubble states.We observed not only the phenomena of dynamically ordered and disordered structures,but also unexpected alternations between them.Our results show that a dissipative system can convert between chaotic structures and ordered structures when tuning global parameters,which is concealed in conventional transport measurements of resistance or conductance.Moreover,charging the objects to study the electrical noise spectrum in collective motions can be an additional approach to revealing dynamic ordering transitions.

New method in information processing for maintaining an efficient dynamic ordered set

This paper investigates how to maintain an efficient dynamic ordered set of bit strings, which is an important problem in the field of information search and information processing. Generally, a dynamic ordered set is required to support 5 essential operations including search, insertion, deletion, max-value retrieval and next-larger-value retrieval. Based on previous research fruits, we present an advanced data structure named rich binary tree （RBT）, which follows both the binary-search-tree property and the digital-search-tree property. Also, every key K keeps the most significant difference bit （MSDB） between itself and the next larger value among K＇s ancestors, as well as that between itself and the next smaller one among its ancestors. With the new data structure, we can maintain a dynamic ordered set in O（L） time. Since computers represent objects in binary mode, our method has a big potential in application. In fact, RBT can be viewed as a general-purpose data structure for problems concerning order, such as search, sorting and maintaining a priority queue. For example, when RBT is applied in sorting, we get a linear-time algorithm with regard to the key number and its performance is far better than quick-sort. What is more powerful than quick-sort is that RBT supports constant-time dynamic insertion/deletion.

Global Existence,Asymptotic Behavior and Uniform Attractors for a Third Order in Time Dynamics

In this paper, a third order（in time） partial differential equation in R^n is con-sidered. By using semigroup method and constructing Lyapunov function, we establish the global existence, asymptotic behavior and uniform attractors in nonhomogeneous case. In addition, we also obtain the results of well-uosedness in semilinear case.

Distributed Solving Linear Algebraic Equations with Switched Fractional Order Dynamics

This paper proposes a novel distributed optimization algorithm with fractional order dynamics to solve linear algebraic equations.Firstly,the authors proposed“Consensus+Projection”flow with fractional order dynamics,which has more design freedom and the potential to obtain a better convergent performance than that of conventional first order algorithms.Moreover,the authors prove that the proposed algorithm is convergent under certain iteration order and step-size.Furthermore,the authors develop iteration order switching scheme with initial condition design to improve the convergence performance of the proposed algorithm.Finally,the authors illustrate the effectiveness of the proposed method with several numerical examples.

Dynamic magnetic behaviors and magnetocaloric effect of the Kagome lattice:Monte Carlo simulations

Based on the Monte Carlo method,we examined the dynamic magnetic behaviors and magnetocaloric effect of a Kagome lattice subjected to the influence of time-dependent oscillating and time-independent magnetic fields.We used the Ising model to describe the Kagome lattice and study the dynamic order parameters,blocking temperature,internal energy,and phase diagrams.The results revealed that exchange coupling increases the stability of the system and the bias field induces order;however,the time-dependent oscillating magnetic field induces disorder.In addition,the magnetocaloric properties,changes in magnetic entropy,and relative cooling power of the Kagome lattice were investigated.

The dynamical contact order:Protein folding rate parameters based on quantum conformational transitions

Protein folding is regarded as a quantum transition between the torsion states of a polypeptide chain.According to the quantum theory of conformational dynamics,we propose the dynamical contact order(DCO) defined as a characteristic of the contact described by the moment of inertia and the torsion potential energy of the polypeptide chain between contact residues.Conse-quently,the protein folding rate can be quantitatively studied from the point of view of dynamics.By comparing theoretical calculations and experimental data on the folding rate of 80 proteins,we successfully validate the view that protein folding is a quantum conformational transition.We conclude that(i) a correlation between the protein folding rate and the contact inertial moment exists;(ii) multi-state protein folding can be regarded as a quantum conformational transition similar to that of two-state proteins but with an intermediate delay.We have estimated the order of magnitude of the time delay;(iii) folding can be classified into two types,exergonic and endergonic.Most of the two-state proteins with higher folding rate are exergonic and most of the multi-state proteins with low folding rate are endergonic.The folding speed limit is determined by exergonic folding.

OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR NEUTRAL PERTURBED DYNAMIC EQUATIONS ON TIME SCALES

In this paper,we discuss the oscillatory behavior of a class of nonlinear neutral perturbed dynamic equations on time scales.Some new oscillation criteria are obtained for such dynamic equations.Finally,an example that dwells upon the sharp conditions of our result is also included.

The Expressibility of First Order Dynamic Logic

This paper resolved an open problem proposed by A .P. Stolboushkin and M .A. Taitslin. We studied the expressibility of first order dynamic logic, and constructed infinite recursive program classes K_1 , K_2, …, RG K_1 K_2 … RF, such that L (RG)<L (K_1)<L (K_2) < … < L (RF), where RG, RF are regular program class and finitely generated recursively enumerable program class respectively, and L (K) is the first order dynamic logic of program class K.

Oscillation Criteria of Second Order Half Linear Delay Dynamic Equations on Time Scales

In this paper, we establish some new oscillation criteria for a non autonomous second order delay dynamic equation （r（t）g（x△（t）））△＋p（t）f（x（τ（t）））=0 on a time scale T. Oscillation behavior of this equation is not studied before. Our results not only apply on differential equations when T=R, difference equations when T=N but can be applied on different types of time scales such as when T=N for q〉1 and also improve most previous results. Finally, we give some examples to illustrate our main results.

Dynamic magnetic properties of Ising graphene-like monolayer

Dynamic magnetic properties of the mixed-spin(3/2,5/2)Ising graphene-like monolayer in an oscillating magnetic field are studied by means of Monte Carlo simulation.The effects of Hamiltonian parameters such as crystal field and time-dependent oscillating magnetic field on the dynamic order parameter,susceptibility and internal energy of the system are well presented and explained.Moreover,much attention has also been dedicated to the phase diagrams with different parameters in order to better comprehend the impacts of these parameters on the critical temperature.Our results reveal that the crystal fields of two sublattices have similar effects on the critical temperature,but the bias field and amplitude of oscillating field have opposite effects on it.We hope that our research can be of guiding significance to the theoretical and experimental studies of graphene-like monolayer.