ABSTRACT
This paper analyzes the complete synchronization of a three-layer Rulkov neuron network model connected by electrical synapses in the same layers and chemical synapses between adjacent layers. The outer coupling matrix of the network is not Laplacian as in linear coupling networks. We develop the master stability function method, in which the invariant manifold of the master stability equations (MSEs) does not correspond to the zero eigenvalues of the connection matrix. After giving the existence conditions of the synchronization manifold about the nonlinear chemical coupling, we investigate the dynamics of the synchronization manifold, which will be identical to that of a synchronous network by fixing the same parameters and initial values. The waveforms show that the transient chaotic windows and the transient approximate periodic windows with increased or decreased periods occur alternatively before asymptotic behaviors. Furthermore, the Lyapunov exponents of the MSEs indicate that the network with a periodic synchronization manifold can achieve complete synchronization, while the network with a chaotic synchronization manifold can not. Finally, we simulate the effects of small perturbations on the asymptotic regimes and the evolution routes for the synchronous periodic and the non-synchronous chaotic network.
ABSTRACT
This paper concerns the intermittent evolution routes to the asymptotic regimes in the Rulkov map. That is, the windows with transient approximate periodic and transient chaotic behaviors occur alternatively before the system reaches the periodic or the chaotic orbits. Meanwhile, the evolution routes to chaotic orbits can be classified into different types according to the windows before reaching asymptotic chaotic states. In addition, the initial values can be regarded as a key factor affecting the asymptotic behaviors and the evolution routes. The effects of the initial values are given by parameter planes, bifurcation diagrams, and waveforms. In order to investigate whether the intermittent evolution routes can be learned by machine learning, some experiments are given to understanding the differences between the trajectories of the Rulkov map generated by the numerical simulations and predicted by the neural networks. These results show that there is about 60% accuracy rate of successfully predicting both the evolution routes and the asymptotic period-3 orbits using a three-layer feedforward neural network, while the bifurcation diagrams can be reconstructed using reservoir computing except a few parameter conditions.
ABSTRACT
This paper takes into account a neuron network model in which the excitatory and the inhibitory Rulkov neurons interact each other through excitatory and inhibitory chemical coupling, respectively. Firstly, for two or more identical or non-identical Rulkov neurons, the existence conditions of the synchronization manifold of the fixed points are investigated, which have received less attention over the past decades. Secondly, the master stability equation of the arbitrarily connected neuron network under the existence conditions of the synchronization manifold is discussed. Thirdly, taking three identical Rulkov neurons as an example, some new results are presented: (1) topological structures that can make the synchronization manifold exist are given, (2) the stability of synchronization when different parameters change is discussed, and (3) the roles of the control parameters, the ratio, as well as the size of the coupling strength and sigmoid function are analyzed. Finally, for the chemical coupling between two non-identical neurons, the transversal system is given and the effect of two coupling strengths on synchronization is analyzed.
ABSTRACT
BACKGROUND: Itai-itai disease primarily results from cadmium (Cd) exposure and is known as one of the four major pollution diseases in Japan. Cd pollution is more serious in several areas of China than in Japan. However, there is still a lack of information regarding the threshold level of Cd exposure for the adverse health effects in the general Chinese population. This study aims to evaluate the reference value of urinary Cd (UCd) for renal dysfunction in a Chinese population as the benchmark dose lower confidence limit (BMDL) based on a large sample survey. METHODS: A total of 6103 participants who lived in five Cd polluted areas of China participated in this study. We analyzed UCd levels as a biomarker of exposure and urinary ß2-microglobulin (Uß2-MG) levels as a renal tubular effect biomarker. The BMD studies were performed using BMD software. The benchmark response (BMR) was defined as a 10% additional risk above the background. RESULTS: There was a positive correlation between the UCd levels and the prevalence of Uß2-MG. The BMD of UCd for Uß2-MG was estimated for each province. The findings showed that the BMD levels were related to the participants' geographic region, which may be partially due to the large differences in Cd exposure level, ethnic group, lifestyle and diet of the sample population in these study areas. The reference level of UCd for the renal effects was further evaluated by combining the five sets of data from all 6103 subjects. The overall BMDLs of UCd for Uß2-MG with an excess risk of 10% were 2.00 µg/g creatinine (µg/g cr) in males and 1.69 µg/g cr in females, which were significantly lower than the World Health Organization (WHO) threshold level of 5 µg/g cr for Cd-related renal effects. CONCLUSIONS: The selection of the sample population and geographic region affected the BMDL evaluation. Based on the findings of this survey of a large sample population, the UCd BMDLs for Uß2-MG in males with BMRs at 10% were 2.00 µg/g cr. The BMD was slightly lower in females, which indicated that females may be relatively more sensitive to Cd exposure than males.