The effects of time delay on the stochastic resonance in feed-forward-loop neuronal network motifs

The dependence of stochastic resonance in the feed-forward-loop neuronal network motifs on the noise and time delay are studied in this paper. By computational modeling, Izhikevich neuron model with the chemical coupling is used to build the triple-neuron feed-forward-loop motifs with all possible motif types. Numerical results show that the correlation between the periodic subthreshold signal’s frequency and the dynamical response of the network motifs is resonantly dependent on the intensity of additive spatiotemporal noise. Interestingly, the excitatory intermediate neuron could induce intermittent stochastic resonance, whereas the inhibitory one weakens its influence on the intermittent mode. More importantly, it is found that the increasing delays can induce the intermittent appearance of regions of stochastic resonance. Based on the effects of the time delay on the stochastic resonance, the reasons and conditions of such intermittent resonance phenomenon are analyzed.     

Heat conduction on the ring: Interface problems with periodic boundary conditions

The classical problem of heat conduction in one dimension on a composite ring is examined. The problem is formulated using the heat equation with periodic boundary conditions. We provide an explicit solution of this problem using the Method of Fokas. The location of the interfaces is known, but neither temperature nor heat flux are prescribed there. Instead, the physical assumption of continuity at the interface is imposed.     

Socle equivalences of weighted surface algebras

We describe the structure and properties of the finite-dimensional symmetric algebras over an algebraically closed field K which are socle equivalent to the general weighted surface algebras of triangulated surfaces, investigated in [11]. In particular, we prove that all these algebras are tame periodic algebras of period 4. The main results of this paper form an essential step towards a classification of all symmetric tame periodic algebras of period 4.     

Existence and stability of periodic solutions of high-order Hopfield neural networks with impulses and delays

By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functions, the global exponential stability and periodicity are investigated for a class of delayed high-order Hopfield neural networks (HHNNs) with impulses, which are new and complement previously known results. Finally, an example with numerical simulation is given to show the effectiveness of the proposed method and results. The numerical simulation shows that our models can occur in many forms of complexities including periodic oscillation and the Gui chaotic strange attractor.     

Fractional Weyl-Riesz Integrodifferentiation of Periodic Functions of Two Variables via the Periodization of the Riesz Kernel

We consider the periodization of the Riesz fractional integrals (Riesz potentials) of two variables and show that already in this case we come across different effects, depending on whether we use the repeated periodization, first in one variable, and afterwards in another one, or the so called double periodization. We show that the naturally introduced doubly-periodic Weyl-Riesz kernel of order 0< f <2 in general coincides with the periodization of the Riesz kernel, the repeated periodization being possible for all 0< f <2 , while the double one is applicable only for 0< f <1 . This is obtained as a realization of a certain general scheme of periodization, both repeated and double versions. We prove statements on coincidence of the corresponding periodic and nonperiodic convolutions and give an application to the case of the Riesz kernel.     

Bäcklund transformations and abundant exact explicit solutions of the Sharma-Tasso-Olver equation

By using an extension of the homogeneous balance method and Maple, the Bäcklund transformations for the Sharma-Tasso-Olver equation are derived. The connections between the Sharma-Tasso-Olver equation and some linear partial differential equations are found. With the aid of the transformations given here and the computer program Maple 12, abundant exact explicit special solutions to the Sharma-Tasso-Olver equation are constructed. In addition to all known solutions re-deriving in a systematic way, several entirely new and more general exact explicit solitary wave solutions can also be obtained. These solutions include (a) the algebraic solitary wave solution of rational function, (b) single-soliton solutions, (c) double-soliton solutions, (d) N-soliton solutions, (e) singular traveling solutions, (f) the periodic wave solutions of trigonometric function type, and (g) many non-traveling solutions. By using the Airy’s function and the Bäcklund transformations obtained here, the exact explicit solution of the initial value problem for the STO equation is presented. The variety of the structure of the solutions for the Sharma-Tasso-Olver equation is illustrated.     

Exact solutions of the combined KdV-Burgers equation with variable coefficients

In this Letter, the exp-function method is used to obtain generalized solitary solutions and periodic solutions of the general types of combined KdV-Burgers equation with variable coefficients. It is shown that the exp-function method via symbolic computation provides a straightforward and powerful mathematical tool for solving nonlinear evolution equations with variable coefficients in mathematical physics.