Exploration of Ideology and Politics Education in Analytical Geometry Under Blending Teaching

With the rapid development and continuous innovation of information technology, traditional teaching model is confronted with great challenge and, sometimes, it is difficult to achieve teaching goals via single offline teaching, especially under the influence of the COVID-19. In this paper, taking space rectangular coordinates and space vector in the course of space analytical geometry as the carrier, ideological and political elements in the course of space analytical geometry is mined via multi-channel from various aspects. Fusion point of ideology and politics elements in space analytical geometry is searched and the implementation path is investigated under blending teaching. The aim is to promote the achievement of the ideology and politics education of space analytical geometry. Keywords: Blending teaching, Ideology and politics education, Analytical geometry DOI: 10.7176/JEP/13-21-15 Publication date:June 30th 202

An Analysis of the Implementation Path of Moral Education in Mathematics under Goal Orientation: Taking "The ellipse and its standard equation" as an example

The practice of moral education in mathematics is an inevitable requirement for the implementation of the fundamental task of establishing moral education. The practice of moral education in mathematics is not conducted blindly. By adopting moral education objectives as the guide, the effectiveness of moral education in the subject can be enhanced. The implementation path of moral education in mathematics was explored in the context of the moral education objectives for the senior secondary level in the "Guidelines for Moral Education in Primary and Secondary Schools", based on the example of the "ellipse and its standard equation". A typical case was used as a carrier; reasonable scenarios were introduced; mathematical thinking and methods were penetrated to focus on the cultural values of mathematics. Keywords: Moral education in mathematics; Goal-oriented; Ellipse DOI: 10.7176/JEP/13-26-06 Publication date:September 30th 202

Multiple Firing Patterns in Coupled Hindmarsh-Rose Neurons with a Nonsmooth Memristor

A model is introduced by coupling two three-dimensional Hindmarsh-Rose models with the help of a nonsmooth memristor. The firing patterns dependent on the external forcing current are explored, which undergo a process from adding-period to chaos. The stability of equilibrium points of the considered model is investigated via qualitative analysis, from which it can be gained that the model has diversity in the number and stability of equilibrium points for different coupling coefficients. The coexistence of multiple firing patterns relative to initial values is revealed, which means that the referred model can appear various firing patterns with the change of the initial value. Multiple firing patterns of the addressed neuron model induced by different scales are uncovered, which suggests that the discussed model has a multiscale effect for the nonzero initial value

Stability Analysis of Fraction-Order Hopfield Neuron Network and Noise-Induced Coherence Resonance

In this paper, dynamical behaviors of fraction-order Hopfield neuron network are investigated. Firstly, Mittag-Leffler stability analysis is carried out and some sufficient conditions are obtained. On the basis of theoretical analysis, two criteria for determining the stability of fraction-order Hopfield neuron network are presented and comparison between them is given by theoretical analysis along with numerical simulation. According to the proposed criteria, by selecting suitable system parameters, it can be obtained that fraction-order Hopfield neuron network can stabilize to the equilibrium point or an attractor, which can be a periodic orbit or two points. Secondly, considering the inevitable noise in the complex environment of neuron network, the effect of noise on the dynamics of fraction-order Hopfield neuron network is discussed via calculating coefficient of variation and numerical simulations. Results suggest that random noise can cause coherence resonance in fraction-order Hopfield neuron network for certain noise intensity

Electrical Activity in a Time-Delay Four-Variable Neuron Model under Electromagnetic Induction

To investigate the effect of electromagnetic induction on the electrical activity of neuron, the variable for magnetic flow is used to improve Hindmarsh–Rose neuron model. Simultaneously, due to the existence of time-delay when signals are propagated between neurons or even in one neuron, it is important to study the role of time-delay in regulating the electrical activity of the neuron. For this end, a four-variable neuron model is proposed to investigate the effects of electromagnetic induction and time-delay. Simulation results suggest that the proposed neuron model can show multiple modes of electrical activity, which is dependent on the time-delay and external forcing current. It means that suitable discharge mode can be obtained by selecting the time-delay or external forcing current, which could be helpful for further investigation of electromagnetic radiation on biological neuronal system

Hidden Dynamics and Hybrid Synchronization of Fractional-Order Memristive Systems

A fractional-order memristive system without equilibrium is addressed. Hidden attractors in the proposed system are discussed and the coexistence of a hidden attractor is found. Via theoretical analysis, the hybrid synchronization of the proposed system with partial controllers is investigated using fractional stability theory. Numerical simulation verifies the validity of the hybrid synchronization scheme

Hidden Dynamics and Hybrid Synchronization of Fractional-Order Memristive Systems

A fractional-order memristive system without equilibrium is addressed. Hidden attractors in the proposed system are discussed and the coexistence of a hidden attractor is found. Via theoretical analysis, the hybrid synchronization of the proposed system with partial controllers is investigated using fractional stability theory. Numerical simulation verifies the validity of the hybrid synchronization scheme

Hidden Dynamics of a New Jerk-like System with a Smooth Memristor and Applications in Image Encryption

Considering the dynamic characteristics of memristors, a new Jerk-like system without an equilibrium point is addressed based on a Jerk-like system, and the hidden dynamics are investigated. When changing system parameter b and fixing other parameters, the proposed system shows various hidden attractors, such as a hidden chaotic attractor (b = 5), a hidden period-1 attractor (b = 3.2), and a hidden period-2 attractor (b = 4). Furthermore, bifurcation analysis suggests that not only parameter b, but also the initial conditions of the system, have an effect on the hidden dynamics of the discussed system. The coexistence of various hidden attractors is explored and different coexistences of hidden attractors can be found for suitable system parameters. Offset boosting of different hidden attractors is discussed. It is observed that offset boosting can occur for hidden chaotic attractor, period-1 attractor, and period-2 attractor, but not for period-3 attractor and period-4 attractor. The antimonotonicity of the proposed system is debated and a full Feigenbaum remerging tree can be detected when system parameters a or b change within a certain range. On account of the complicated dynamics of the proposed system, an image encryption scheme is designed, and its encryption effectiveness is analyzed via simulation and comparison