Stability analysis of multi-group deterministic and stochastic epidemic models with vaccination rate

We discuss in this paper a deterministic multi-group MSIR epidemic model with a vaccination rate, the basic reproduction number R0, a key parameter in epidemiology, is a threshold which determines the persistence or extinction of the disease. By using Lyapunov function techniques, we show if R0 is greater than 1 and the deterministic model obeys some conditions, then the disease will prevail, the infective persists and the endemic state is asymptotically stable in a feasible region. If R0 is less than or equal to 1, then the infective disappear so the disease dies out. In addition, stochastic noises around the endemic equilibrium will be added to the deterministic MSIR model in order that the deterministic model is extended to a system of stochastic ordinary differential equations. In the stochastic version, we carry out a detailed analysis on the asymptotic behavior of the stochastic model. In addition, regarding the value of R0, when the stochastic system obeys some conditions and R0 is greater than 1, we deduce the stochastic system is stochastically asymptotically stable.Finally, the deterministic and stochastic model dynamics are illustrated through computer simulations.     

Topologically inequivalent orbits induced by noise

In this Letter we extend the concept of stochastic resonance. We show that in forced excitable systems noise can be responsible for the appearance of recurrences presenting a robust topological organization inequivalent to the periodic orbits of the deterministic system. As in stochastic resonance, these new structures are most pronounced at an optimal noise intensity.     

Detecting nonlinearity of action surface EMG signal

The action surface EMG (ASEMG) signal contains the electrical properties of limb muscle contraction that undergo many complex transitions in limb different movement states; however, because of the small data nature of this kind signal, it is not clear whether its essence is stochastic or deterministic nonlinear (even chaotic). In this Letter, we show for the first time that ASEMG has deterministic nonlinear character by using the surrogate data method. Furthermore, we study the nonlinear dynamic features of ASEMG by computing its correlation dimension and applying correlation dimension as test statistics. These results indicate that ASEMG is a high-dimension nonlinear signal (even chaotic). In addition, this Letter improves the surrogate data method based on Fourier transform (FT) algorithm to avoid limitations of the previous FT algorithm.     

Distinguishing fingerprints of hyperchaotic and stochastic dynamics in optical chaos from a delayed opto-electronic oscillator

In the dynamics of optical systems, one commonly needs to cope with the problem of coexisting deterministic and stochastic components. The separation of these components is an important, although difficult, task. Often the time scales at which determinism and noise dominate the system's dynamics differ. In this Letter we propose to use information-theory-derived quantifiers, more precisely, permutation entropy and statistical complexity, to distinguish between the two behaviors. Based on experiments of a paradigmatic opto-electronic oscillator, we demonstrate that the time scales at which deterministic or noisy behavior dominate can be identified. Supporting numerical simulations prove the accuracy of this identification.     

Formulation of the Korteweg–de Vries and the Burgers equations expressing mass transports from the generalized Kawasaki–Ohta equation

By generalization of the Kawasaki–Ohta equation representing the interface dynamics, we report formulation of equations, which express mass transports, deterministic and stochastic, for nonlinear lattices. The equations are written characteristically by flow variable representations defined in the Letter. We found that the KdV equation and the Burgers equation, formulated by the flow variables, express mass transports in hydrodynamics and in stochastic processes, respectively. The representations lead to the conclusion that in nonequilibria we should observe a change not in a concentration but in concentration flows.     

Identification of fractional-order systems via a switching differential evolution subject to noise perturbations

In this Letter, a differential evolution variant, called switching DE (SDE), has been employed to estimate the orders and parameters in incommensurate fractional-order chaotic systems. The proposed algorithm includes a switching population utilization strategy, where the population size is adjusted dynamically based on the solution-searching status. Thus, this adaptive control method realizes the identification of fractional-order Lorenz, Lü and Chen systems in both deterministic and stochastic environments, respectively. Numerical simulations are provided, where comparisons are made with five other State-of-the-Art evolutionary algorithms (EAs) to verify the effectiveness of the proposed method.     

A Spatial Stochastic Model for Virus Dynamics

We introduce a spatial stochastic model for virus dynamics. We show that if the death rate of infected cells increases too fast with the virus load the virus dies out. This is in sharp contrast with what happens in the (non-spatial deterministic) basic model for virus dynamics. AMS 1991 Subject Classification: 60K35     

Bounding the quality of stochastic oscillations in population models

We analyze general two-species stochastic models, of the kind generally used for the study of population dynamics. Although usually defined a priori, the deterministic version of these models can be obtained as the infinite volume limit of many stochastic models (which are necessarily defined by more parameters than the deterministic one). It is known that damped oscillations in a deterministic model usually correspond to oscillatory-like fluctuations in their deterministic counterparts. The quality of these “oscillations" depends on details of each stochastic model. We show, however, that the parameters of the deterministic system are generally enough to obtain very good bounds for the quality of “oscillations" in any of its stochastic counterparts. These bounds are shown to depend on only one dimensionless parameter.     

On stochastic parameter estimation using data assimilation

Data assimilation-based parameter estimation can be used to deterministically tune forecast models. This work demonstrates that it can also be used to provide parameter distributions for use by stochastic parameterization schemes. While parameter estimation is (theoretically) straightforward to perform, it is not clear how one should physically interpret the parameter values obtained. Structural model inadequacy implies that one should not search for a deterministic “best” set of parameter values, but rather allow the parameter values to change as a function of state; different parameter values will be needed to compensate for the state-dependent variations of realistic model inadequacy. Over time, a distribution of parameter values will be generated and this distribution can be sampled during forecasts. The current work addresses the ability of ensemble-based parameter estimation techniques utilizing a deterministic model to estimate the moments of stochastic parameters. It is shown that when the system of interest is stochastic the expected variability of a stochastic parameter is biased when a deterministic model is employed for parameter estimation. However, this bias is ameliorated through application of the Central Limit Theorem, and good estimates of both the first and second moments of the stochastic parameter can be obtained. It is also shown that the biased variability information can be utilized to construct a hybrid stochastic/deterministic integration scheme that is able to accurately approximate the evolution of the true stochastic system.     

气-固界面作用物理模型的确定性实现方法

针对最新发展的气-固界面作用物理模型,提出一种确定性计算方法.算法的核心是:针对离散速度空间分布函数,采用确定性算法计算出单轮气-固碰撞作用的散射核函数矩阵,并通过考虑吸引势阱作用和迭代累加多次气-固碰撞作用,物理地反映气体分子入射/反射速度分布函数在气-固界面上的变化.与现有基于Monte Carlo随机采样的实现方...     

Structure functions in a model of turbulent energy dissipation

A stochastic activity-transfer model, previously proposed to apply to turbulence, is studied and simulated on a 256×256 lattice. Introduction of random self-activation does not allow stable fronts to develop in the limit of small growth probability. By assigning discrete density values equal to the threshold values in a related continuous and deterministic model, the structure functions for distancesr in the lattice are calculated. They have a functional form different from the power behavior which in the case of the deterministic version was interpreted as another sign of self-organized criticality. Future studies of these and other models may be facilitated by the algorithm developed for structure function calculations.     

Individual-based model for coevolving competing populations

Classical models for competition between two species usually predict exclusion or divergent evolution of resource exploitation. However, recent experimental data show that coexistence is possible for very similar species competing for the same resources without niche partition. Motivated by this experimental challenge to classical competition theory, we propose an individual-based stochastic competition model, which is essentially a modification of a deterministic Lotka-Volterra type model. The proposed model of competition dynamics incorporates the effects of a discrete genotype, which determines the individual's adaptation to the environment, as well as its interaction with the other species.     

哺乳动物生理振荡中的最佳内噪声效应

基于哺乳动物生理振子模型，构造了相应的介观随机模型，研究了该系统中内噪声对基因振荡的影响．结果发现通过内噪声随机共振的机制，随机的基因振荡可以在最佳内噪声水平处达到最佳状态．同时，还发现存在一个中间的系统尺度使得随机模型表现出比确定性模型更宽的有效振荡区域，这说明了内噪声增强了体系的鲁帮性．讨论了这些效应可能的生理意义．     

Emergence of fractal scale-free networks from stochastic evolution on the Cayley tree

An unexpected recognition of fractal topology in some real-world scale-free networks has evoked again an interest in the mechanisms stimulating their evolution. To explain this phenomenon a few models of a deterministic construction as well as a probabilistic growth controlled by a tunable parameter have been proposed so far. A quite different approach based on the fully stochastic evolution of the fractal scale-free networks presented in this Letter counterpoises these former ideas. It is argued that the diffusive evolution of the network on the Cayley tree shapes its fractality, self-similarity and the branching number criticality without any control parameter. The last attribute of the scale-free network is an intrinsic property of the skeleton, a special type of spanning tree which determines its fractality.     

Secure communication scheme based on asymptotic model of deterministic randomness

In this Letter, we introduce a new cryptosystem by integrating the asymptotic model of deterministic randomness with the one-way coupled map lattice (OCML) system. The key space, the encryption efficiency, and the security under various attacks are investigated. With the properties of deterministic randomness and spatiotemporal dynamics, the new scheme can improve the security to the order of computational precision, even when the lattice size is three only. Meanwhile, all the lattices can be fully utilized to increase the encryption speed.     

A General Metric for the Similarity of Both Stochastic and Deterministic System Dynamics

Many problems in the study of dynamical systems—including identification of effective order, detection of nonlinearity or chaos, and change detection—can be reframed in terms of assessing the similarity between dynamical systems or between a given dynamical system and a reference. We introduce a general metric of dynamical similarity that is well posed for both stochastic and deterministic systems and is informative of the aforementioned dynamical features even when only partial information about the system is available. We describe methods for estimating this metric in a range of scenarios that differ in respect to contol over the systems under study, the deterministic or stochastic nature of the underlying dynamics, and whether or not a fully informative set of variables is available. Through numerical simulation, we demonstrate the sensitivity of the proposed metric to a range of dynamical properties, its utility in mapping the dynamical properties of parameter space for a given model, and its power for detecting structural changes through time series data.     

Stochastic persistence and stationary distribution in a Holling-Tanner type prey-predator model

In this paper, we study a stochastic predator-prey model with Beddington-DeAngelis type functional response and logistic growth for predators. The deterministic model is already well-studied and we recall some important results here. We construct the stochastic model from the deterministic model by introducing multiplicative noise terms into the growth equations of prey and predator populations. For the stochastic model, we show that the system admits unique positive global solution starting from the positive initial value. Then we prove that the system is strongly persistent in mean when the intensity of environmental forcing is less than some threshold magnitudes. Finally, we show that the system has a stationary distribution under certain parametric restrictions. Numerical simulations are carried out to substantiate the analytical results.     

Waves and energy in random elastic guided media through the stochastic wave finite element method

Energy propagation in random viscoelastic media is considered in this Letter. The forced response of uncertain waveguide subject to time harmonic loading is treated. This energy model is based on a spectral approach called the “Stochastic Wave Finite Element” (SWFE) method which is detailed in this Letter. Assuming that the random properties are spatially homogeneous in the media, the SWFE is a hybridization of the deterministic wave finite element and a parametric probabilistic approach. The proposed model is applicable in a wide frequency band with reduced time consumption. Numerical examples show the effectiveness of the proposed approach to predict the statistics of kinematic and quadratic variables of guided wave propagation. The results are compared to Monte Carlo simulations.     

Non-Equilibrium Behaviour in Unidirectionally Coupled Map Lattices

A spatially one dimensional coupled map lattice with a local and unidirectional coupling is introduced. This model is studied analytically by a perturbation theory that is valid for small coupling strength. In parameter space three phases with different ergodic behaviour are observed. Via coarse graining the deterministic model is mapped to a stochastic spin model that can be described by a master equation. Because of the anisotropic coupling non-equilibrium behaviour is found on the coarse grained level. However, the stationary statistical properties of the spin dynamics can still be described with a nearest neighbour Ising model whereby the ordering is predominantly antiferromagnetic.     

Flow reversal in a simple dynamical model of turbulence

In this Letter, we study a simple hydrodynamical model showing abrupt flow reversals at random times. For a suitable range of parameters, we show that the dynamics of flow reversal is accurately described by stochastic differential equations, where the noise represents the effect of turbulence.