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1.
We consider spatially extended systems of interacting nonlinear Hawkes processes modeling large systems of neurons placed in Rd and study the associated mean field limits. As the total number of neurons tends to infinity, we prove that the evolution of a typical neuron, attached to a given spatial position, can be described by a nonlinear limit differential equation driven by a Poisson random measure. The limit process is described by a neural field equation. As a consequence, we provide a rigorous derivation of the neural field equation based on a thorough mean field analysis.  相似文献   
2.
Paraquat (PQ) poisoning seriously harms the health of humanity. An effective diagnostic method for paraquat poisoned patients is a crucial concern. Nevertheless, it's difficult to identify the patients with low intake of PQ or delayed treatment. Here, a new efficient diagnostic approach to integrate machine learning and gas chromatography-mass spectrometry (GC–MS), named GEE, is proposed to identify the PQ poisoned patients. First, GC–MS provides the original data that efficiently identified the paraquat-poisoned patients. According to the high dimensionality of the original data, in the second stage, the chaos enhanced grey wolf optimization (EGWO) is adopted to search the optimal feature sets to improve the accuracy of identification. Finally, the extreme learning machine (ELM) is used to identify the PQ poisoned patients. To efficiently evaluate the proposed method, four measures were used in our experiments and comparisons were made with six other methods. The PQ-poisoned patients and robust volunteers can be well identified by GEE and the values of AUC, accuracy, sensitivity and specificity were 95.14%, 93.89%, 94.44% and 95.83%, respectively. Our experimental results demonstrated that GEE had better performance and might serve as a novel candidate diagnosis of PQ-poisoned patients.  相似文献   
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In this paper we analyze a delay-induced predator–prey–parasite model with prey harvesting, where the predator–prey interaction is represented by Leslie–Gower type model with type II functional response. Infection is assumed to spread horizontally from one infected prey to another susceptible prey following mass action law. Spreading of disease is not instantaneous but mediated by a time lag to take into account the time required for incubation process. Both the susceptible and infected preys are subjected to linear harvesting. The analysis is accomplished in two phases. First we analyze the delay-induced predator–prey–parasite system in absence of harvesting and proved the local & global dynamics of different (six) equilibrium points. It is proved that the delay has no influence on the stability of different equilibrium points except the interior one. Delay may cause instability in an otherwise stable interior equilibrium point of the system and larger delay may even produce chaos if the infection rate is also high. In the second phase, we explored the dynamics of the delay-induced harvested system. It is shown that harvesting of prey population can suppress the abrupt fluctuations in the population densities and can stabilize the system when it exceeds some threshold value.  相似文献   
5.
《随机分析与应用》2013,31(4):815-837
We find the chaos expansion of local time ? T (H)(x,·) of fractional Brownian motion with Hurst coefficient H∈(0,1) at a point x∈R d . As an application we show that when H 0 d<1 then ? T (H)(x,·)∈L 2(μ). Here μ denotes the probability law of B (H) and H 0=max{H 1,…,H d }. In particular, we show that when d=1 then ? T (H)(x,·)∈L 2(μ) for all H∈(0,1).  相似文献   
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7.
The generation and synchronization of broadband optical chaos in dual-path optically injected (DPOI) semiconductor lasers (SLs) are numerically demonstrated. The effective bandwidth enhancement is achieved up to about 35.84 GHz, under appropriate injection strength and frequency detuning. We systematically study and compare the bandwidth enhancement in single-path optically injected SLs (SPOI-SLs) and DPOI-SLs, and find that better performance can be obtained for the latter over a larger parameter span. Furthermore, two schemes for synchronization of bandwidth-enhanced chaos generated in two similar or identical (twin) DPOI-SLs are proposed, where the twins are driven by a common DPOI signal injected from another chaotic SL. High-quality chaos synchronization, an isochronous type, is observed between the twin DPOI-SLs. Also, the effect of parameter mismatch and frequency detuning is numerically examined. The simple technique of bandwidth enhancement using dual-path injection may pave way for various applications such as high-speed random number generators (RNGs) and chaos-based communications.  相似文献   
8.
The physics of granular matter is one of the big questions in science. Granular matter serves as a prototype of collective systems far from equilibrium and fundamental questions remain. At the same time, an understanding of granular matter has tremendous practical importance. Among practical problems, granular mixing and its interplay with segregation is arguably at the top of the list in terms of impact. Granular mixing in three-dimensional systems is complicated, as flow induces segregation by particle size or density. Several approaches and points of view for analysis are possible in principle, ranging from continuum to discrete. Flow and segregation in three-dimensional systems is seemingly complicated; however, to a reasonable approximation, all of the dynamics takes place in a thin flowing surface layer. This observation, coupled with key experimental results, leads to a simple, compact and extensible continuum-based dynamical systems framework applicable to time-periodic flow in quasi-two-dimensional tumblers and three-dimensional systems (such as spheres and cubes) rotated about one or more axes of rotation. The case of time-periodic systems, in its simplest version, can be viewed as a mapping of a domain into itself. The placement of periodic points can be investigated using symmetry concepts; the character of the periodic points and associated manifolds provides a skeleton for the flow and a template for segregation processes occurring in the flow.  相似文献   
9.
Most existing social learning models assume that there is only one underlying true state. In this work, we consider a social learning model with multiple true states, in which agents in different groups receive different signal sequences generated by their corresponding underlying true states. Each agent updates his belief by combining his rational self-adjustment based on the external signals he received and the influence of his neighbors according to their communication. We observe chaotic oscillation in the belief evolution, which implies that neither true state could be learnt correctly by calculating the largest Lyapunov exponents and Hurst exponents.  相似文献   
10.
In this paper, an effective self-embedding fragile watermarking scheme is presented. The watermark is generated by encoding the DCT coefficients of each 2 × 2 block and embedded into another block according to the block mapping. A non-linear chaotic sequence is used for generating the block mapping which can enhance the security of the algorithm. An improved tamper localization and recovery algorithm are performed. The experiment results show that the watermarked image has a high average peak signal-to-noise ratio. Furthermore, the tamper region can be successfully localized and exactly recovered, even if for the content-only tampering.  相似文献   
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