This paper presents the finding of a novel chaotic system with one source and two saddle-foci in a simple three-dimensional （3D） autonomous continuous time Hopfield neural network. In particular, the system with one...This paper presents the finding of a novel chaotic system with one source and two saddle-foci in a simple three-dimensional （3D） autonomous continuous time Hopfield neural network. In particular, the system with one source and two saddle-foci has a chaotic attractor and a periodic attractor with different initial points, which has rarely been reported in 3D autonomous systems. The complex dynamical behaviours of the system are further investigated by means of a Lyapunov exponent spectrum, phase portraits and bifurcation analysis. By virtue of a result of horseshoe theory in dynamical systems, this paper presents rigorous computer-assisted verifications for the existence of a horseshoe in the system for a certain parameter.展开更多
This paper proposes fractional-order systems for Hopfield Neural Network(HNN).The so-called Predictor Corrector Adams Bashforth Moulton Method(PCABMM)has been implemented for solving such systems.Graphical comparisons...This paper proposes fractional-order systems for Hopfield Neural Network(HNN).The so-called Predictor Corrector Adams Bashforth Moulton Method(PCABMM)has been implemented for solving such systems.Graphical comparisons between the PCABMM and the Runge-Kutla Method(RKM)solutions for the classical HNN reveal that the proposed technique is one of the powerful tools for handling these systems.To determine all Lyapunov exponents for them,the Benettin-Wolf algorithm has been involved in the PCABMM.leased on such algorithm,the Lyapunov exponents as a function of a given parameter and as another function of the fractional-order have been described,the intermittent chaos for these systems has been explored.A new result related to the Mittag-Leffler stability of some nonlinear Fractional-order Hopfield Neural Network(FoHNN)systems has been shown.Besides,the description and the dynamic analysis of those phenomena have been discussed and verified theoretically and numerically via illustrating the phase portraits and the Lyapunov exponents'diagrams.展开更多
In this paper the nonlinear dynamical behaviour of a quantum cellular neural network （QCNN） by coupling Josephson circuits was investigated and it was shown that the QCNN using only two of them can cause the onset o...In this paper the nonlinear dynamical behaviour of a quantum cellular neural network （QCNN） by coupling Josephson circuits was investigated and it was shown that the QCNN using only two of them can cause the onset of chaotic oscillation. The theoretical analysis and simulation for the two Josephson-circuits-coupled QCNN have been done by using the amplitude and phase as state variables. The complex chaotic behaviours can be observed and then proved by calculating Lyapunov exponents. The study provides valuable information about QCNNs for future application in high-parallel signal processing and novel chaotic generators.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.60774088)the Program for New Century Excellent Talents in University of China(NCET)+1 种基金the Science & Technology Research Key Project of Educational Ministry of China(Grant No.107024)the Foundation of the Application Base and Frontier Technology Research Project of Tianjin(Grant No.08JCZDJC21900)
文摘This paper presents the finding of a novel chaotic system with one source and two saddle-foci in a simple three-dimensional （3D） autonomous continuous time Hopfield neural network. In particular, the system with one source and two saddle-foci has a chaotic attractor and a periodic attractor with different initial points, which has rarely been reported in 3D autonomous systems. The complex dynamical behaviours of the system are further investigated by means of a Lyapunov exponent spectrum, phase portraits and bifurcation analysis. By virtue of a result of horseshoe theory in dynamical systems, this paper presents rigorous computer-assisted verifications for the existence of a horseshoe in the system for a certain parameter.
基金supporting this work by the University Ajman Grant:2Q20-COVID-19-08.
文摘This paper proposes fractional-order systems for Hopfield Neural Network(HNN).The so-called Predictor Corrector Adams Bashforth Moulton Method(PCABMM)has been implemented for solving such systems.Graphical comparisons between the PCABMM and the Runge-Kutla Method(RKM)solutions for the classical HNN reveal that the proposed technique is one of the powerful tools for handling these systems.To determine all Lyapunov exponents for them,the Benettin-Wolf algorithm has been involved in the PCABMM.leased on such algorithm,the Lyapunov exponents as a function of a given parameter and as another function of the fractional-order have been described,the intermittent chaos for these systems has been explored.A new result related to the Mittag-Leffler stability of some nonlinear Fractional-order Hopfield Neural Network(FoHNN)systems has been shown.Besides,the description and the dynamic analysis of those phenomena have been discussed and verified theoretically and numerically via illustrating the phase portraits and the Lyapunov exponents'diagrams.
基金Project supported by the Natural Science Foundation of Shaanxi Province, China （Grant No 2005F20） and the Innovation Funds of the College of Science, Air Force University of Engineering, China （Grant No 2007B003）.
文摘In this paper the nonlinear dynamical behaviour of a quantum cellular neural network （QCNN） by coupling Josephson circuits was investigated and it was shown that the QCNN using only two of them can cause the onset of chaotic oscillation. The theoretical analysis and simulation for the two Josephson-circuits-coupled QCNN have been done by using the amplitude and phase as state variables. The complex chaotic behaviours can be observed and then proved by calculating Lyapunov exponents. The study provides valuable information about QCNNs for future application in high-parallel signal processing and novel chaotic generators.
