In this paper, a SEIR epidemic model for the COVID-19 is built according to some general control strategies, such as hospital, quarantine and external input Based on the data of Hubei province, the particle swarm optimization (PSO) algorithm is applied to estimate the parameters of the system We found that the parameters of the proposed SEIR model are different for different scenarios Then, the model is employed to show the evolution of the epidemic in Hubei province, which shows that it can be used to forecast COVID-19 epidemic situation Moreover, by introducing the seasonality and stochastic infection the parameters, nonlinear dynamics including chaos are found in the system Finally, we discussed the control strategies of the COVID-19 based on the structure and parameters of the proposed model

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SEIR modeling of the COVID-19 and its dynamics.

A fast image encryption algorithm based on compressive sensing and hyperchaotic map

Chaotic dynamics is widely used to design pseudo-random number generators and for other applications such as secure communications and encryption. This paper aims to study the dynamics of discrete-time chaotic maps in the digital (i.e., finite-precision) domain. Differing from the traditional approaches treating a digital chaotic map as a black box with different explanations according to the test results of the output, the dynamical properties of such chaotic maps are first explored with a fixed-point arithmetic, using the Logistic map and the Tent map as two representative examples, from a new perspective with the corresponding state-mapping networks (SMNs). In an SMN, every possible value in the digital domain is considered as a node and the mapping relationship between any pair of nodes is a directed edge. The scale-free properties of the Logistic map's SMN are proved. The analytic results are further extended to the scenario of floating-point arithmetic and for other chaotic maps. Understanding the network structure of a chaotic map's SMN in digital computers can facilitate counteracting the undesirable degeneration of chaotic dynamics in finite-precision domains, helping also classify and improve the randomness of pseudo-random number sequences generated by iterating chaotic maps.

Dynamic Analysis of Digital Chaotic Maps via State-Mapping Networks

We provide, calibrate and test a realistic model of the spread of SARS-Cov-2 in an economy with different risks related to age and sectors. The model considers hospital congestion and response of individuals adjusting their behavior to the virus' spread. We measure precisely the size of these effects using real data for Italy on intensive care capacity and mobility decisions; thus our claim is that the tradeoffs we estimate are quantitatively, rather than qualitatively, approximately correct. We characterize the policies of containment of the epidemic that are efficient with respect to number of fatalities and GDP loss. Prudent policies of gradual return to work may save many lives with limited economic costs, as long as they differentiate by age group and risk sector. More careful behavior of individuals induced by the perceived cost of infection may contribute to further reduce fatalities.

/pdf/restarting-the-economy-while-saving-lives-under-covid-19-17szhveoub.pdf

Restarting the Economy While Saving Lives Under COVID-19

The study of dynamics on artificial neurons and neuronal networks is of great significance to understand brain functions and develop neuromorphic systems. Recently, memristive neuron and neural network models offer great potential in the investigation of neurodynamics. Many chaotic dynamics including chaos, transient chaos, hyperchaos, coexisting attractors, multistability, and extreme multistability have been researched based on the memristive neurons and neural networks. In this review, we firstly introduce the basic definition of chaotic dynamics and review several traditional artificial neuron and neural network models. Then we categorize memristive neuron and neural network models with different biological function mechanisms into five types: memristive autapse neuron, memristive synapse-coupled bi-neuron network, memristive synaptic weight neural network, neuron under electromagnetic radiation, and neural network under electromagnetic radiation. The modeling mechanisms of each type are explained and described in detail. Furthermore, the pioneer works and some recent important papers related to those types are introduced. Finally, some open problems in this field are presented to further explore future work.

Review on chaotic dynamics of memristive neuron and neural network

The realization of real memristor makes it be a very popular topic in recent years. However, the topic about discrete memristor model is rarely discussed. In this paper, a discrete memristor model is proposed based on the difference theory, and the three fingerprints characteristics are proved for this model according to the definition of the generalized memristor. This discrete model is applied to Henon map, and we designed a new chaotic map called the discrete memristor-based Henon map. Its dynamical behaviors are analyzed by attractor phase diagram, bifurcation diagram, Lyapunov exponent spectrum, and spectral entropy complexity algorithm. Simulation results show the performance of Henon map is improved by applying the discrete memristor.

A discrete memristor model and its application in Hénon map

Research on fractional-order discrete chaotic systems has grown in recent years, and chaos synchronization of such systems is a new topic. To address the deficiencies of the extant chaos synchronization methods for fractional-order discrete chaotic systems, we proposed an improved particle swarm optimization algorithm for the parameter identification. Numerical simulations are carried out for the Henon map, the Cat map, and their fractional-order form, as well as the fractional-order standard iterated map with hidden attractors. The problem of choosing the most appropriate sample size is discussed, and the parameter identification with noise interference is also considered. The experimental results demonstrate that the proposed algorithm has the best performance among the six existing algorithms and that it is effective even with random noise interference. In addition, using two samples offers the most efficient performance for the fractional-order discrete chaotic system, while the integer-order discrete chaotic system only needs one sample.

Parameter Identification of Fractional-Order Discrete Chaotic Systems

The parameter estimation of a chaotic system is an important issue in nonlinear science, and it has gained increased attention in recent years. However, the existing estimation methods must be based on the initial values known in the original system. Yet the initial values cannot be obtained in many cases, which is not conducive to the reconstruction and control of chaotic systems. In addition, these methods are unable to provide enough precision for high-dimensional complex chaotic systems. In this paper, a parameter estimation method with unknown initial values is developed, and a new algorithm called the chaos behaved particle swarm optimization algorithm is proposed. Three highlights, namely chaos initialization, special inertia weight and chaos search, are introduced into the algorithm. The simulation experiments are carried out for three complex chaotic systems, including two typical fractional-order hyperchaotic systems and a fractional-order multi-directional multi-scroll chaotic attractor system. Based on the results, the method proposed in this paper demonstrates more effectiveness and advantages than the other four existing algorithms.

Yuexi Peng

Papers

SEIR modeling of the COVID-19 and its dynamics.

A discrete memristor model and its application in Hénon map

Parameter Identification of Fractional-Order Discrete Chaotic Systems

Parameter estimation of a complex chaotic system with unknown initial values

Detecting chaos in fractional-order nonlinear systems using the smaller alignment index