Synchronization coexistence in a Rulkov neural network based on locally active discrete memristor

At present, many neuron models have been proposed, which can be divided into discrete neuron models and continuous neuron models. Discrete neuron models have the advantage of faster simulation speed and the ease of understanding complex dynamic phenomena. Due to the properties of memorability, nonvolatility, and local activity, locally active discrete memristors(LADMs) are also suitable for simulating synapses. In this paper, we use an LADM to mimic synapses and establish a Rulkov neural network model. It is found that the change of coupling strength and the initial state of the LADM leads to multiple firing patterns of the neural network. In addition, considering the influence of neural network parameters and the initial state of the LADM, numerical analysis methods such as phase diagram and timing diagram are used to study the phase synchronization. As the system parameters and the initial states of the LADM change, the LADM coupled Rulkov neural network exhibits synchronization transition and synchronization coexistence.

Adaptive Biorthogonal Local Discrete Cosine Transform for Interference Excision in Direct Sequence Spread Spectrum Communications

A novel time-frequency domain interference excision technique is proposed. The technique is based on adaptive biorthogonal local discrete cosine trans form (BLDCT). It uses a redundant library of biorthogonal local discrete cosine bases and an efficient concave cost function to match the transform basis to the interfering signal. The main advantage of the algorithm over conventional trans form domain excision algorithms is that the basis functions are not fixed but ca n be adapted to the time-frequency structure of the interfering signal. It is w e ll suited to transform domain compression and suppression of various types of in terference. Compared to the discrete wavelet transform (DWT) that provides logar ithmic division of the frequency bands, the adaptive BLDCT can provide more flex ible frequency resolution. Thus it is more insensitive to variations of jamming frequency. Simulation results demonstrate the improved bit error rate (BER) perf ormance and the increased robustness of the receiver.

Ground-roll separation of seismic data based on morphological component analysis in twodimensional domain

Ground roll is an interference wave that severely degrades the signal-to-noise ratio of seismic data and affects its subsequent processing and interpretation.In this study,according to differences in morphological characteristics between ground roll and reflected waves,we use morphological component analysis based on two-dimensional dictionaries to separate ground roll and reflected waves.Because ground roll is characterized by lowfrequency,low-velocity,and dispersion,we select two-dimensional undecimated discrete wavelet transform as a sparse representation dictionary of ground roll.Because of a strong local correlation of the reflected wave,we select two-dimensional local discrete cosine transform as the sparse representation dictionary of reflected waves.A sparse representation model of seismic data is constructed based on a two-dimensional joint dictionary then a block coordinate relaxation algorithm is used to solve the model and decompose seismic record into reflected wave part and ground roll part.The good effects for the synthetic seismic data and application of real seismic data indicate that when using the model,strong-energy ground roll is considerably suppressed and the waveform of the reflected wave is effectively protected.

Discrete Littlewood–Paley–Stein Characterization and L^2 Atomic Decomposition of Local Hardy Spaces

Usually, the condition that T is bounded on L^2(R^n) is assumed to prove the boundedness of an operator T on a Hardy space. With this assumption, one only needs to prove the uniformly boundness of T on atoms, since T(f)=∑iλi T(ai), provided that f =∑iλiai in L^2(R^n), where ai is an L^2 atom of this Hardy space. So far, the L^2 atomic decomposition of local Hardy spaces h^p(R^n), 0 < p ≤ 1, hasn't been established. In this paper, we will solve this problem, and also show that h^p(R^n) can also be characterized by discrete Littlewood-Paley functions.

Simulation of Incompressible Viscous Flows by Local DFD-Immersed Boundary Method

A local domain-free discretization-immersed boundary method(DFDIBM)is presented in this paper to solve incompressible Navier-Stokes equations in the primitive variable form.Like the conventional immersed boundary method(IBM),the local DFD-IBM solves the governing equations in the whole domain including exterior and interior of the immersed object.The effect of immersed boundary to the surrounding fluids is through the evaluation of velocity at interior and exterior dependent points.To be specific,the velocity at interior dependent points is computed by approximate forms of solution and the velocity at exterior dependent points is set to the wall velocity.As compared to the conventional IBM,the present approach accurately implements the non-slip boundary condition.As a result,there is no flow penetration,which is often appeared in the conventional IBM results.The present approach is validated by its application to simulate incompressible viscous flows around a circular cylinder.The obtained numerical results agree very well with the data in the literature.

HIGH RESOLUTION SCHEMES FOR CONSERVATION LAWS AND CONVECTION-DIFFUSION EQUATIONS WITH VARYING TIME AND SPACE GRIDS

This paper presents a class of high resolution local time step schemes for nonlinear hyperbolic conservation laws and the closely related convection-diffusion equations, by projecting the solution increments of the underlying partial differential equations （PDE） at each local time step. The main advantages are that they are of good consistency, and it is convenient to implement them. The schemes are L^∞ stable, satisfy a cell entropy inequality, and may be extended to the initial boundary value problem of general unsteady PDEs with higher-order spatial derivatives. The high resolution schemes are given by combining the reconstruction technique with a second order TVD Runge-Kutta scheme or a Lax-Wendroff type method, respectively. The schemes are used to solve a linear convection-diffusion equation, the nonlinear inviscid Burgers＇ equation, the one- and two-dimensional compressible Euler equations, and the two-dimensional incompressible Navier-Stokes equations. The numerical results show that the schemes are of higher-order accuracy, and efficient in saving computational cost, especially, for the case of combining the present schemes with the adaptive mesh method [15]. The correct locations of the slow moving or stronger discontinuities are also obtained, although the schemes are slightly nonconservative.