D3 Dihedral Logistic Map of Fractional Order

In this paper, the D3 dihedral logistic map of fractional order is introduced. The map presents a dihedral symmetry D3. It is numerically shown that the construction and interpretation of the bifurcation diagram versus the fractional order requires special attention. The system stability is determined and the problem of hidden attractors is analyzed. Furthermore, analytical and numerical results show that the chaotic attractor of integer order, with D3 symmetries, looses its symmetry in the fractional-order variant.

Study on dry friction vibration model based on energy method

Purpose This study aims to establish the friction vibration model. Design/methodology/approach The friction vibration experiment was carried out on a pin disk friction tester. The causes of friction vibration are discussed, and the friction vibration model is established based on the energy method. Findings The experimental and simulation results show that the main cause of friction vibration is the nonlinear change of friction coefficient; degree of the friction vibration has a positive relationship with the friction relative velocity and normal contact positive pressure; the proposed friction vibration model is highly consistent in chaotic attractor and time-frequency distribution map and can well predict friction vibration. Originality/value The proposed friction vibration model is highly consistent in chaotic attractor and time-frequency distribution map and can well predict friction vibration.

Large fractal dimension of chaotic at tractor for earthquake sequence near Nurek reservoir

Fractal dimension of the chaotic attractor for earthquake sequence in Nurek dam based on 22.000 earthquakes detected during the period 1976-87 has been studied for this total period of observations as well as for the period from December 1977 to December 1987. The second period excluded increased seismic activity during second stage of filling the reservoir. Large fractal dimensions of the chaotic at tractor of 8.3 and 7.3 were found for the respective period which suggests the complexity of earthquake .dynamics in this region as compared to Koyna reservoir.

D3 Dihedral Logistic Map of Fractional Order

In this paper the D 3 dihedral logistic map of fractional order is introduced. The map 1 presents a dihedral symmetry D 3 . It is numerically shown that the construction and interpretation 2 of the bifurcation diagram versus the fractional order require special attention. The system stability 3 is determined and the problem of hidden attractors is analyzed. Also, analytical and numerical 4 results show that the chaotic attractor of integer order, with D 3 symmetries, looses its symmetry 5 in the fractional-order variant.

Multistable Dynamics in a Hopfield Neural Network Under Electromagnetic Radiation and Dual Bias Currents

This paper investigates a Hopfield neural network (HNN) under the simulation of external electromagnetic radiation and dual bias currents, in which the fluctuation of magnetic flux across the neuron membrane is used to emulate the influence of electromagnetic radiation. Utilizing conventional analytical methods, the basic properties of the proposed Hopfield neural network are discussed. Due to the addition of electromagnetic radiation and dual bias currents, the Hopfield neural network shows high sensitivity to system parameters and initial conditions. The proposed Hopfield neural network possesses multistability with periodic attractor, quasi-periodic attractor, chaotic attractor and transient chaotic attractor, and all of the attractors are hidden attractors because there is no equilibrium point in the system. In particular, when the neuron membrane magnetic flux is different, the system can present transient chaos with different chaotic times. More interestingly, with the change of system parameters, the proposed Hopfield neural network can exhibit parallel bifurcation behaviors. Finally, the Multisim simulation and hardware experiment results based on discrete electronic components are conducted to support the numerical ones. These results could give useful information to the study of nonlinear dynamic characteristics of the Hopfield neural network.

An Economy Can Have a Lorenz-Type Chaotic Attractor

This paper presents a stylized construction of an economy with price dynamics described in tâtonnement process. Based on the well-known SMD theorem, it is shown that this model exhibits the same dynamical behavior as the famous Lorenz-type chaotic attractor.

A Hidden Chaotic System with Multiple Attractors

This paper reports a hidden chaotic system without equilibrium point. The proposed system is studied by the software of MATLAB R2018 through several numerical methods, including Largest Lyapunov exponent, bifurcation diagram, phase diagram, Poincaré map, time-domain waveform, attractive basin and Spectral Entropy. Seven types of attractors are found through altering the system parameters and some interesting characteristics such as coexistence attractors, controllability of chaotic attractor, hyperchaotic behavior and transition behavior are observed. Particularly, the Spectral Entropy algorithm is used to analyze the system and based on the normalized values of Spectral Entropy, the state of the studied system can be identified. Furthermore, the system has been implemented physically to verify the realizability.

Modeling of Chaotic Processes by Means of Antisymmetric Neural ODEs

The main goal of this work is to construct an algorithm for modeling chaotic processes using special neural ODEs with antisymmetric matrices (antisymmetric neural ODEs) and power activation functions (PAFs). The central part of this algorithm is to design a neural ODEs architecture that would guarantee the generation of a stable limit cycle for a known time series. Then, one neuron is added to each equation of the created system until the approximating properties of this system satisfy the well-known Kolmogorov theorem on the approximation of a continuous function of many variables. In addition, as a result of such an addition of neurons, the cascade of bifurcations that allows generating a chaotic attractor from stable limit cycles is launched. We also consider the possibility of generating a homoclinic orbit whose bifurcations lead to the appearance of a chaotic attractor of another type. In conclusion, the conditions under which the found attractor adequately simulates the chaotic process are discussed. Examples are given.