一个新的四维混沌系统理论分析与电路实现

分析了一个新的复杂的四维混沌系统的基本特性，该系统每个方程中包含一个三次交叉乘积项，共有9个平衡点，它们相对于原点和坐标轴具有完美的对称性，并且相对于线性特性和不变流形具有很好的相似性.描述了两个同时共存的对称双翼吸引子.最后，设计了一个模拟电路来实现这个新的四维混沌系统，表明数值仿真和电路实现具有很好的一致性，同时说明在应用上由于频率不同导致的仿真与物理实现之间的重要区别. 关键词： 四维混沌系统 Lyapunov 指数 共存双翼吸引子 电路实现     

Modeling and dynamics of double Hindmarsh-Rose neuron with memristor-based magnetic coupling and time delay

The firing of a neuron model is mainly affected by the following factors:the magnetic field, external forcing current, time delay, etc. In this paper, a new time-delayed electromagnetic field coupled dual Hindmarsh-Rose neuron network model is constructed. A magnetically controlled threshold memristor is improved to represent the self-connected and the coupled magnetic fields triggered by the dynamic change of neuronal membrane potential for the adjacent neurons. Numerical simulation confirms that the coupled magnetic field can activate resting neurons to generate rich firing patterns, such as spiking firings, bursting firings, and chaotic firings, and enable neurons to generate larger firing amplitudes. The study also found that the strength of magnetic coupling in the neural network also affects the number of peaks in the discharge of bursting firing. Based on the existing medical treatment background of mental illness, the effects of time lag in the coupling process against neuron firing are studied. The results confirm that the neurons can respond well to external stimuli and coupled magnetic field with appropriate time delay, and keep periodic firing under a wide range of external forcing current.     

提升学生信息提取能力的若干策略

信息提取是学生利用物理知识和方法解决具体问题的关键环节,是学生物理学科核心素养的外在表现之一.以浙江省2021年和2022年高考(选考)试题为例,从物理学科核心素养视角提出助推学生信息提取的策略.     

Hopf bifurcation analysis and circuit implementation for a novelfour-wing hyper-chaotic system

In the paper, a novel four-wing hyper-chaotic system is proposed and analyzed. A rare dynamic phenomenon is found that this new system with one equilibrium generates a four-wing-hyper-chaotic attractor as parameter varies. The system has rich and complex dynamical behaviors, and it is investigated in terms of Lyapunov exponents, bifurcation diagrams, Poincare′ maps, frequency spectrum, and numerical simulations. In addition, the theoretical analysis shows that the system undergoes a Hopf bifurcation as one parameter varies, which is illustrated by the numerical simulation. Finally, an analog circuit is designed to implement this hyper-chaotic system.     

一个新的三维混沌系统的分析、电路实现及同步

中心流形理论提供了一个将高维系统降维研究的方法，应用该理论研究了一个新的混沌系统的基本特性，给出中心流形上流方程，分析这个新的混沌系统的叉式分岔.通过构建电路实现了该混沌系统,从而验证了系统的混沌行为，证实了混沌吸引子的存在.同时说明了由于电路信号频率与数值信号频率的不同所带来的数值仿真与物理实现之间在应用上有着重要区别.最后利用单变量反馈控制方法实现了新系统的同步控制，并给出了完整的同步实现电路. 关键词： 三维混沌系统 中心流形 电路实现 同步     

指向科学思维素养水平评价的路径研究

对学生通过物理学科的学习所达到的物理学科核心素养水平进行科学的、可信的、精准的评价,能了解学生素养水平的习得情况,发现存在的问题并及时进行学习干预,进而促进学生素养水平的提升.以物理学科四大素养要素中的“科学思维”为例,从评价的指向、试题的命制和学生的分析三方面对科学思维素养水平评价的路径进行研究.     

Optimal control strategy for COVID-19 concerning both life and economy based on deep reinforcement learning

At present, the global COVID-19 is still severe. More and more countries have experienced second or even third outbreaks. The epidemic is far from over until the vaccine is successfully developed and put on the market on a large scale. Inappropriate epidemic control strategies may bring catastrophic consequences. It is essential to maximize the epidemic restraining and to mitigate economic damage. However, the study on the optimal control strategy concerning both sides is rare, and no optimal model has been built. In this paper, the Susceptible-Infectious-Hospitalized-Recovered (SIHR) compartment model is expanded to simulate the epidemic's spread concerning isolation rate. An economic model affected by epidemic isolation measures is established. The effective reproduction number and the eigenvalues at the equilibrium point are introduced as the indicators of controllability and stability of the model and verified the effectiveness of the SIHR model. Based on the Deep Q Network (DQN), one of the deep reinforcement learning (RL) methods, the blocking policy is studied to maximize the economic output under the premise of controlling the number of infections in different stages. The epidemic control strategies given by deep RL under different learning strategies are compared for different reward coefficients. The study demonstrates that optimal policies may differ in various countries depending on disease spread and anti-economic risk ability. The results show that the more economical strategy, the less economic loss in the short term, which can save economically fragile countries from economic crises. In the second or third outbreak stage, the earlier the government adopts the control strategy, the smaller the economic loss. We recommend the method of deep RL to specify a policy which can control the epidemic while making quarantine economically viable.     

一个四翼混沌吸引子

在新的四维混沌系统中数值观察到四翼混沌吸引子，然而，通过进一步分析发现，该四翼吸引子并非真实的，实际上它是上、下两个共存的双翼混沌吸引子，他们各自有独立的混沌吸引域，由于其位置靠得太近和数值误差产生的一种假象.通过引入一个线性状态反馈控制项，系统的一些相似性被破坏，受控系统能产生穿越上下吸引域界限的对角双翼混沌吸引子，进一步，随着动力学模态的演化，上下混沌吸引子与对角混沌吸引子融合成一个真正的四翼混沌吸引子.最后，通过比较该四翼混沌吸引子的系统、Lorenz系统、Chua氏电路等混沌信号的频谱发现，四翼混沌吸引子的系统信号具有极宽的频谱带宽，该特性在通讯加密等工程应用中具有重要价值. 关键词： 四维混沌系统 双翼吸引子 四翼吸引子 频谱分析     

Hyper-chaos encryption using convolutional masking and model free unmasking

In this paper, during the masking process the encrypted message is convolved and embedded into a Qi hyper-chaotic system characterizing a high disorder degree. The masking scheme was tested using both Qi hyper-chaos and Lorenz chaos and indicated that Qi hyper-chaos based masking can resist attacks of the filtering and power spectrum analysis, while the Lorenz based scheme fails for high amplitude data. To unmask the message at the receiving end, two methods are proposed. In the first method, a model-free synchronizer, i.e. a multivariable higher-order differential feedback controller between the transmitter and receiver is employed to de-convolve the message embedded in the receiving signal. In the second method, no synchronization is required since the message is de-convolved using the information of the estimated derivative.