Chaos in social learning with multiple true states

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.     

Mean field limits for nonlinear spatially extended Hawkes processes with exponential memory kernels

We consider spatially extended systems of interacting nonlinear Hawkes processes modeling large systems of neurons placed in ${\mathbb{R}}^d$ 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.     

The lifetime of CFC substitutes studied by a network trained with chaotic mapping modified genetic algorithm and DFT calculations

The hydrohaloalkanes have attracted much attention as potential substitutes of chlorofluorocarbons (CFCs) that deplete the ozone layer and lead to great high global warming. Having a short atmospheric lifetime is very important for the potential substitutes that may also induce ozone depletion and yield high global warming gases to be put in use. Quantitative structure–activity relationship (QSAR) studies were presented for their lifetimes aided by the quantum chemistry parameters including net charges, Mulliken overlaps, E _HOMO and E _LUMO based on the density functional theory (DFT) at B3PW91 level, and the C-H bond dissociation energy based on AM1 calculations. Outstanding features of the logistic mapping, a simple chaotic system, especially the inherent ability to search the space of interest exhaustively have been utilized. The chaotic mapping aided genetic algorithm artificial neural network training scheme (CGANN) showed better performance than the conventional genetic algorithm ANN training when the structure of the data set was not favorable. The lifetimes of HFCs and HCs appeared to be greatly dependent on their energies of the highest occupied molecular orbitals. The perference of the RMSRE comparing to RMSE as objective function of ANN training was better for the samples of interest with relatively short lifetimes. C₂H₆ and C₃H₈ as potential green substitutes of CFCs present relatively short lifetimes.     

Amplitude modulation control of escape from a potential well

We demonstrate the effectiveness of periodic amplitude modulations in controlling (suppressing and enhancing) escape from a potential well through the universal model of a damped Helmholtz oscillator subjected to an external periodic excitation (the escape-inducing excitation) whose amplitude is periodically modulated (the escape-controlling excitation). Analytical and numerical results show that this multiplicative control works reliably for different subharmonic resonances between the two periodic excitations involved, and that its effectiveness is comparable to those of different methods of additive control. Additionally, we demonstrate the robustness of the multiplicative control against the presence of low-intensity Gaussian noise.     

The potential energy surface and chaos in 2D Hamiltonian systems

We provide a new insight into the relationship between the geometric property of the potential energy surface and chaotic behavior of 2D Hamiltonian dynamical systems, and give an indicator of chaos based on the geometric property of the potential energy surface by defining Mean Convex Index (MCI). We also discuss a model of unstable Hamiltonian in detail, and show our results in good agreement with HBLSL's (Horwitz, Ben Zion, Lewkowicz, Schiffer and Levitan) new Riemannian geometric criterion.     

噪音对光学图象浑沌相位列阵加密和解密的影响

本文提出了一种用浑沌相位列阵对光学图象加密和解密的方法,并重点分析了加法高斯白噪音对光学图象浑沌相位列阵加密和解密的影响.通过计算机模拟发现加密后的图象与原图象相比,抗振幅噪音的能力增强,而抗相位噪音的能力下降.在一定信噪比范围内,相位噪音是影响解密图象质量的主要因素.     

Consistent Lyapunov exponent Estimation for one-dimensional dynamical systems

Summary  The author proves the consistency of a nearest neighbor estimator of the Lyapunov exponent for a general class of one-dimensional ergodic dynamical systems. The author shows that this estimator has good practical properties on a set of simulations.     

Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification

In this paper, the adaptive synchronization and lag synchronization are considered for uncertain dynamical system with time delay based on parameter identification and a novel control method is then further given using the Lyapunov functional method. With this new and effective method, parameter identification and lag synchronization can be achieved simultaneously. Simulation results are given to justify the theoretical analysis in this paper.