Convergence to a terrace solution in multistable reaction–diffusion equation with discontinuities

In this paper we address the large-time behavior of solutions of bistable and multistable reaction–diffusion equation with discontinuities around the stable steady states. We show that the solution always converges to a special solution, which may either be a traveling wave in the bistable case, or more generally a terrace (i.e. a collection of stacked traveling waves with ordered speeds) in the multistable case.     

Gated Polling Systems with Lévy Inflow and Inter-Dependent Switchover Times: A Dynamical-Systems Approach

We study asymmetric polling systems where: (i) the incoming workflow processes follow general Lévy-subordinator statistics; and, (ii) the server attends the channels according to the gated service regime, and incurs random inter-dependentswitchover times when moving from one channel to the other. The analysis follows a dynamical-systems approach: a stochastic Poincaré map, governing the one-cycle dynamics of the polling system is introduced, and its statistical characteristics are studied. Explicit formulae regarding the evolution of the mean, covariance, and Laplace transform of the Poincaré map are derived. The forward orbit of the maps transform – a nonlinear deterministic dynamical system in Laplace space – fully characterizes the stochastic dynamics of the polling system. This enables us to explore the long-term behavior of the system: we prove convergence to a (unique) steady-state equilibrium, prove the equilibrium is stationary, and compute its statistical characteristics.     

忆阻Hopfield神经网络动力学分析及其电路实现

提出一种超多稳态忆阻Hopfield神经网络, 它仅包含3个神经元和一个多稳态忆阻突触。从理论上分析神经网络的耗散性和平衡点的稳定性, 并利用分岔图、李雅普诺夫指数谱和相位图等数值方法分析不同忆阻突触耦合强度对神经网络动力学的影响。网络参数固定时, 揭示与初始状态值密切相关的超多稳态性动力学行为。最后, 设计忆阻Hopfield神经网络的模拟等效电路, 并通过PSIM电路仿真验证MATLAB数值仿真结果。     

Low threshold voltage asymmetric antiferroelectric liquid crystal cells

Asymmetric antiferroelectric liquid crystal displays (AAFLCD) are attractive since they show a very well defined off state and fast switching time. Moreover, they can be driven by a simple biasless DC compensated waveform. The electrooptical response of an AAFLCD allows for new addressing modes, including quasi-static intermediate greyscales maintained without applying a field and passively addressed multiplexed high-frequency displays and spatial light modulators. A new kind of asymmetric cells have been obtained by using fluorinated block copolymer (FBC) alignment, which enhances surface segregation and provides a low energy surface. In this work we combine FBC alignment with antiferroelectric liquid crystal mixtures containing strongly electronegative fluorinated components. Threshold voltages for the antiferroelectric-ferroelectric phase transition as low as 3 volts are observed. We report the time evolution of the shift of the electro-optical response.     

Derivative-free Greeks for the Barndorff-Nielsen and Shephard stochastic volatility model

We derive derivative-free formulas for the Delta and other Greeks of options written on an asset modelled by a geometric Brownian motion with stochastic volatility of Barndorff-Nielsen and Shephard type. The method applies the Malliavin calculus in Wiener space which moves differentiation of the payoff function of the option to a random weight function. Our method paves the way for simple Monte Carlo approaches, illustrated by several numerical examples.     

Multivariate time changes for Lévy asset models: Characterization and calibration

We build a theoretical framework for multivariate subordination of Brownian motions, with a common and an idiosyncratic component. This follows economic intuition and introduces generalizations of some well known multivariate Lévy processes for financial applications: the compound Poisson, NIG, Variance Gamma and CGMY. In most cases we obtain the characteristic function in closed form. The extension is first kept parsimonious, by adding one parameter only. The empirical fit of (linear) dependence is then increased, by allowing for dependent Brownian motions.     

Firing activities in a fractional-order Hindmarsh-Rose neuron with multistable memristor as autapse

Considering the fact that memristors have the characteristics similar to biological synapses, a fractional-order multistable memristor is proposed in this paper. It is verified that the fractional-order memristor has multiple local active regions and multiple stable hysteresis loops, and the influence of fractional-order on its nonvolatility is also revealed. Then by considering the fractional-order memristor as an autapse of Hindmarsh-Rose (HR) neuron model, a fractional-order memristive neuron model is developed. The effects of the initial value, external excitation current, coupling strength and fractional-order on the firing behavior are discussed by time series, phase diagram, Lyapunov exponent and inter spike interval (ISI) bifurcation diagram. Three coexisting firing patterns, including irregular asymptotically periodic (A-periodic) bursting, A-periodic bursting and chaotic bursting, dependent on the memristor initial values, are observed. It is also revealed that the fractional-order can not only induce the transition of firing patterns, but also change the firing frequency of the neuron. Finally, a neuron circuit with variable fractional-order is designed to verify the numerical simulations.     

On martingale characterizations for some generalized space fractional Poisson processes

We obtain martingale characterizations for the generalized space fractional Poisson process (GSFPP) and for counting processes with Bern?tein intertimes. These serve as extensions of the Watanabe's characterization for the classical homogenous Poisson process. The corresponding assertion for the space fractional Poisson process (SFPP) is obtained as a particular case of our results.     

Potential Theory of Special Subordinators and Subordinate Killed Stable Processes

In this paper we introduce a large class of subordinators called special subordinators and study their potential theory. Then we study the potential theory of processes obtained by subordinating a killed symmetric stable process in a bounded open set D with special subordinators. We establish a one-to-one correspondence between the nonnegative harmonic functions of the killed symmetric stable process and the nonnegative harmonic functions of the subordinate killed symmetric stable process. We show that nonnegative harmonic functions of the subordinate killed symmetric stable process are continuous and satisfy a Harnack inequality. We then show that, when D is a bounded κ-fat set, both the Martin boundary and the minimal Martin boundary of the subordinate killed symmetric stable process in D coincide with the Euclidean boundary ∂D. The research of this author is supported in part by MZOS grant 0037107 of the Republic of Croatia and in part by a joint US-Croatia grant INT 0302167.