Global multistability and analog circuit implementation of an adapting synapse-based neuron model

This paper proposes a MEMS resonant pressure sensor through implementing an out-of-plane repulsive (levitation) force to enhance the sensor detection threshold and consequently widen its sensing range. 2D and 3D finite-element simulations are conducted and compared to some available experimental data. The simulated results show an increase in the generated levitation force as outstanding merit owing to the added side upper electrodes. The levitation force is then further increased by lateral spacing optimization in association with the assumed applied voltage, which decreases the overall size (footprint) as well. The dynamical behavior around the static equilibrium is first numerically solved using the so-called shooting technique and then compared with an available online simulation tool: the “Matcont” package. The simulated results prove the capability of the online simulator to capture the dynamic response of the resonant micro-sensor when approaching its respective bifurcation points where the stable and unstable branches collide, when in contrary, the shooting technique failed to get the dynamic responses when passing by these bifurcations. Thanks to the fast converging outcomes of the “Matcont” online simulation equipped with simultaneous stability analysis, a comprehensive analysis of the micro-sensor dynamical response is conducted. Three sensing mechanisms as: measurements of frequency shift, amplitude alternation, and amplitude rise/fall near a bifurcation region are evaluated and characterized. Along with enumerating the strengths of the proposed sensor over the conventional capacitive pressure sensors, the advantage of measuring the amplitude rise/fall near the corresponding bifurcation region comparing to the two other sensing mechanisms is detailed, and its possible failure for performance repeatability is resolved by means of the slow-varying frequency sweep. Unlike the traditional parallel-plate configuration in which only one-side frequency shift is observed, in this proposed design, two-sides frequency shift is detected, and accordingly, the reinitialization is categorized based on that. As compared to the conventional MEMS pressure sensor, this revisited design equipped with the suggested sensing mechanism offers wider tunability and sensing range, resolution power enhancement, and simplification of the signal processing circuit.

     

Dynamics explore of an improved HR neuron model under electromagnetic radiation and its applications

The influence of electromagnetic field to neuron firing rhythm is not negligible. In order to investigate the behavior mechanism, a five-dimensional neuron model based on the Faraday's law of electromagnetic induction is improved by introducing magnetic flux variables and electric field variables on the three-dimensional Hindmarsh–Rose (HR) neuron model, and then, its rich dynamics and application in image encryption are discussed. Specifically, the equilibrium point distribution is analyzed using Matcont software and it is found that there are subcritical Hopf bifurcation and coexisting mode firing first. Second, numerical simulations are performed in terms of two-parameter bifurcation, ISI bifurcation, the maximum Lyapunov exponent and firing sequences, and the experimental results show that the new model exhibits various firing rhythms. The rich dynamic behaviors make the model more suitable for application in image encryption. So in the end, a grayscale image encryption scheme containing five parts called sparse, compression calculation, forward diffusion, rank scrambling and backward diffusion is designed by combining with the compressive sensing theory. The security analysis results show that the designed encryption scheme not only has excellent compression performance and high security, but also displays faster encryption speed. That is to say, the algorithm can be applied to the field of real encryption owning to the advantages of the lower costs of data transmission and higher efficiency of encryption. It is worth mentioning that the influence of different dimensional compression methods on the encryption and reconstruction effects is analyzed for the first time. The research results of this paper provide some ideas for perfecting the neuron model, revealing the influence of electromagnetic field on biological nervous system, and the excellent performance of the new neuron model provides theoretical guidance and experimental basis for the practical application of digital image encryption.

     

Dynamical analysis and FPGA implementation of a chaotic oscillator with fractional-order memristor components

Memristor-based chaotic and hyperchaotic systems are of great interest in the recent years, and addition of meminductor and memcapacitors to the family has widened the applications. In this paper, we propose a new chaotic system with fractional-order memristor and memcapacitor components. Nonlinear chaotic properties of the proposed system are investigated with equilibrium points, eigenvalues, Lyapunov exponents, bifurcation and bicoherence plots. We show that a small model disturbance can make the system to show self-excited and hidden attractors. We use the Adomian Decomposition method for implementing the proposed system in Field Programmable Gate Arrays.     

Dynamical analysis and control strategies of an SIVS epidemic model with imperfect vaccination on scale-free networks

Nonlinear Dynamics - Vaccination is an effective method to prevent the spread of infectious diseases. In this paper, we develop an SIVS epidemic model with degree-related transmission rates and...     

Complete dynamical analysis of a neuron model

In-depth understanding of the generic mechanisms of transitions between distinct patterns of the activity in realistic models of individual neurons presents a fundamental challenge for the theory of applied dynamical systems. The knowledge about likely mechanisms would give valuable insights and predictions for determining basic principles of the functioning of neurons both isolated and networked. We demonstrate a computational suite of the developed tools based on the qualitative theory of differential equations that is specifically tailored for slow–fast neuron models. The toolkit includes the parameter continuation technique for localizing slow-motion manifolds in a model without need of dissection, the averaging technique for localizing periodic orbits and determining their stability and bifurcations, as well as a reduction apparatus for deriving a family of Poincaré return mappings for a voltage interval. Such return mappings allow for detailed examinations of not only stable fixed points but also unstable limit solutions of the system, including periodic, homoclinic and heteroclinic orbits. Using interval mappings we can compute various quantitative characteristics such as topological entropy and kneading invariants for examinations of global bifurcations in the neuron model.     

A moderate deflection composite helicopter rotor blade model with an improved cross-sectional analysis

The compatibility between a composite beam cross-sectional analysis based on the variational asymptotic approach, and a helicopter rotor blade model which is part of a comprehensive rotorcraft analysis code is examined. It was found that the finite element cross-sectional analysis code VABS can be combined with a moderate deflection rotor blade model in spite of the differences between the formulations. The new YF/VABS rotor blade model accounts for arbitrary cross-sectional warping, in-plane stresses, and moderate deflections. The YF/VABS composite rotor blade model was validated against experimental data and various rotor blade analyses by examining displacements and stresses under static loads, as well as aeroelastic stability of a composite rotor blade in hover, and forward flight vibratory hubloads of a four bladed composite rotor.     

Effect of spatially correlated noise on stochastic synchronization in globally coupled FitzHugh-Nagumo neuron systems

The phenomenon of stochastic synchronization in globally coupled FitzHugh-Nagumo (FHN) neuron system subjected to spatially correlated Gaussian noise is investigated based on dynamical mean-field approximation (DMA) and direct simulation (DS). Results from DMA are in good quantitative or qualitative agreement with those from DS for weak noise intensity and larger system size. Whether the consisting single FHN neuron is staying at the resting state, subthreshold oscillatory regime, or the spiking state, our investigation shows that the synchronization ratio of the globally coupled system becomes higher as the noise correlation coefficient increases, and thus we conclude that spatial correlation has an active effect on stochastic synchronization, and the neurons can achieve complete synchronization in the sense of statistics when the noise correlation coefficient tends to one. Our investigation also discloses that the noise spatial correlation plays the same beneficial role as the global coupling strength in enhancing stochastic synchronization in the ensemble. The result might be useful in understanding the information coding mechanism in neural systems.     

Dynamical response,information transition and energy dependence in a neuron model driven by autapse

Autapses are a class of special synapses of neurons. In those neurons, their axons are not connected to the dendrites of other neurons but are attached to their own cell bodies. The output signal of a neuron feeds back to itself, thereby allowing the neuronal firing behavior to be self-tuned. Autapses can adjust the firing accuracy of a neuron and regulate the synchronization of a neuronal system. In this paper, we investigated the information capacity and energy efficiency of a Hodgkin–Huxley neuron in the noisy signal transmission process regulated by delayed inhibitory chemical autapse for different feedback strengths and delay times. We found that the information transmission, coding efficiency, and energy efficiency are maximized when the delay time is half of the input signal period. With the increase in the inhibitory strength of autapse, this maximization is increasingly obvious. Therefore, we propose that the inhibitory autaptic structure can serve as a mechanism and enable neural information processing to be energy efficient.

     

Dynamical analysis and circuit implementation of a DC/DC single-stage boost converter with memristance load

Nonlinear Dynamics - The DC/DC boost converter can exhibit nonlinear phenomena like chaos and periodic motion, which are influenced by system parameters, topological structure, load and pulse...     

Dynamical analysis of compositions

This paper analyzes musical opus from the point of view of two mathematical tools, namely the entropy and the multidimensional scaling (MDS). The Fourier analysis reveals a fractional dynamics, but the time rhythm variations are diluted along the spectrum. The combination of time-window entropy and MDS copes with the time characteristics and is well suited to treat a large volume of data. The experiments focus on a large number of compositions classified along three sets of musical styles, namely ??Classical??, ??Jazz??, and ??Pop & Rock?? compositions. Without lack of generality, the present study describes the application of the tools and the sets of musical compositions in a methodology leading to clear conclusions, but extensions to other possibilities are straightforward. The results reveal significant differences in the musical styles, demonstrating the feasibility of the proposed strategy and motivating further developments toward a dynamical analysis of musical compositions.     

FitzHugh-Nagumo神经元网络的同步振荡与联想记忆

本文研究由FitzHugh—Nagumo神经元所组成的脉动神经元网络的同步与联想记忆恢复。基于神经元微观生理结构，本文给出具有空间随机分布延时的神经元间耦合，而这种随机分布延时描述了脉动信号从突触前神经元到突触后神经元在轴突上传播所需要的时间。记忆由空时发放的神经元集群表达，在噪声涨落的作用下，系统取得了对不完整输入的记忆恢复。     

A particle suspension model: an unstructured finite-volume implementation

In this paper, a modified particle temperature model for concentrated suspensions is proposed, which allows for the shear-induced migration of particles. The migration is modelled by a convection–diffusion equation, derived from the particle mass and momentum conservation. The model is implemented in an unstructured finite volume method and is utilized to investigate the shear-induced particle migration in channel flow. The profiles and the evolution of the velocity, concentration and particle temperature along the channel are presented. The entrance lengths needed to reach a fully developed profile of the corresponding field variables are also checked against different averaged concentrations and different relative particle radii. Comparison with available experimental data is made whenever possible.     

Dynamical model and control of a small-world network with memory

This paper proposes a dynamical model of influence volume of small-world-network with memory to investigate the effects of multiple delays on network dynamics. We calculate the influence volume covered by the spreading quantity, discuss the effect of finite size on the network dynamics, and then give the saturate time. The dynamical control is also investigated by introducing the delayed state feedback to simulate the adaptivity of network. With properly chosen delay and gain in feedback path, the controlled model may have stable equilibrium, periodic solution, quasi-periodic solution, or a complex chaotic attractor from a sequence of period-doubling bifurcations. It shows delayed feedback control may find important applications in the management and dynamical control of complex networks.     

Bread dough rheology: an improved damage function model

We describe an improved damage function model for bread dough rheology. The model has relatively few parameters, all of which can easily be found from simple experiments as discussed in this paper. Small deformations in the linear region are described by a gel-like power-law memory function. Then, we consider a set of large non-reversing deformations—stress relaxation after a step of shear, steady shearing and elongation beginning from rest and biaxial stretching. With the introduction of a revised strain measure which includes a Mooney–Rivlin term, all of these motions can be well described by the damage function described previously. For reversing step strains, larger amplitude oscillatory shearing and recoil we present a discussion which shows how the damage function model can be applied in these cases.     

An improved nonlinear model for an automotive shock absorber

A new physical model for a shock absorber is presented which provides a more realistic representation of the stiffness characteristics than previous simple models. The new model is validated on experimental data.     

一类改进最大熵方法的可调参数分析

在结构可靠性分析中,引入含可调参数的转换函数能对传统的最大熵方法进行改进,获得更高的失效概率预测精度。但是,此可调参数的最佳取值很难确定。针对这一问题,引入概率守恒方程,从功能函数转换前后所得概率密度函数出发,建立其最大熵值的变化关系,给出转换前后最大熵值之差的理论形式。通过对三种典型单调非线性转换函数开展算例研究,发现功能函数转换前后的最大熵值之差与转换函数的最佳可调参数值有关。改变可调参数值驱使最大熵值之差变化的同时,改进最大熵方法能遍历到更好的失效概率估计值。