Dynamics of the Forced Thirring Instanton with Two Forcing Terms

Geometrical properties of local dynamics in Hamiltonian systems: The Generalized Alignment Index (GALI) method

Memristor-coupled asymmetric neural networks: Bionic modeling, chaotic dynamics analysis and encryption application

The scope of this work is to perform a numerical investigation of the orbital dynamics for a test particle in the pseudo-Newtonian Hill problem. Large two-dimensional sets of initial conditions of prograde and retrograde orbits are investigated. The orbits are classified as bounded (chaotic, sticky or regular), escaping and collision orbits. The smaller alignment index (SALI) method is used to identify chaotic orbits. Additionally, the influence of the energy (or equivalently the value of the Jacobi constant) and of the Schwarzschild radius on the orbital structure of the system are determined. Our numerical results are compared with related previous ones, corresponding to the classical version of the Hill problem.

We present a comparison of different numerical techniques for the integration of variational equations. The methods presented can be applied to any autonomous Hamiltonian system whose kinetic energy is quadratic in the generalized momenta, and whose potential is a function of the generalized positions. We apply the various techniques to the well-known H´enon-Heiles system, and use the Smaller Alignment Index (SALI) method of chaos detection to evaluate the percentage of its chaotic orbits. The accuracy and the speed of the integration schemes in evaluating this percentage are used to investigate the numerical efficiency of the various techniques.

Application of the SALI chaos detection method to accelerator mappings

The escape dynamics of the stars in a barred galaxy composed of a spherically symmetric central nucleus, a bar, a flat thin disk and a dark matter halo component is investigated by using a realistic three degrees of freedom (3-dof) dynamical model. Modern colour-coded diagrams are used for distinguishing between bounded and escaping motion. In addition, the smaller alignment index (SALI) method is deployed for determining the regular, sticky or chaotic nature of bounded orbits. We reveal the basins of escape corresponding to the escape through the two symmetrical escape channels around the Lagrange points $L_2$ and $L_3$ and also we relate them with the corresponding distribution of the escape times of the orbits. Furthermore, we demonstrate how the stable manifolds, around the index-1 saddle points, accurately define the fractal basin boundaries observed in the colour-coded diagrams. The development scenario of the fundamental vertical Lyapunov periodic orbit is thoroughly explored for obtaining a more complete view of the unfolding of the singular behaviour of the dynamics at the cusp values of the parameters. Finally, we examine how the combination of the most important parameters of the bar (such as the semi-major axis and the angular velocity) influences the observed stellar structures (rings and spirals) which are formed by escaping stars guided by the invariant manifolds near the saddle points.

The dynamic behavior of an optical micro ring resonator (OMRR) with an amplitude modulator positioned in the micro ring is investigated quantitatively by adopting a recently introduced quantifier, the permutation entropy (PE).The effects of modulation depth are focused on, and the roles of input power are considered.The two-dimensional (2D) maps of PE showing dependence on both modulation depth and input power are presented as well.PE values nearly increase with modulation depth.On the other hand, the optimal value of input power is achieved when the PE reaches its maximum.Thus, PE can successfully quantify the dynamics of modulated OMRR.Selecting the parameters in the region with high PE values would contribute to the complexity-enhanced OMRR-based chaotic communication systems.

We study the dynamic behavior of a variant of Hartley’s circuit from numerical and experimental viewpoints. First, we observed the transition from regular to chaotic behavior considering as parameter controls either the values of resistors or inductors. We experimentally obtained the phase space of the circuits for different values of the parameter control and using specialized software for electronic circuits, we corroborated the experimental results. Finally, we characterized the circuit’s dynamical behavior with a related dynamical system determining phase spaces, bifurcation diagrams, and Lyapunov exponents. The phase spaces enabled us to have a qualitative insight into the dynamical behavior (regular or chaotic) when observing the shape of the related attractors. The bifurcation diagrams indicated how the dynamics evolve from regular to chaotic behavior or vice versa. Moreover, we observed the bifurcation cascade of doubling periods in the route to chaos. The largest Lyapunov exponent permitted us to eventually determine the chaotic or regular behavior of the system quantitatively, once more finding a good agreement with our experimental results.

In this work, the interesting dynamics of coupled nonlinear memristor-based oscillators in ring configuration are explored. The mathematical models are derived to describe the possible cases of employing identical or different nonlinearities. Analytical and numerical techniques, involving perturbation methods, normal forms, phase portraits, and Lyapunov exponents are used to investigate various types of dynamical behaviors along with their stability regions in parameters space. The effects of time-delayed coupling on the proposed system are numerically studied. It is demonstrated that the coupled oscillators show rich dynamics including periodic orbits, quasiperiodicity, two-dimensional, and three-dimensional tori.

Piecewise-type nonlinearities, such as clutch dampers in a torsional system, induce complex nonlinear dynamic behaviors that resemble super- and sub-harmonic responses. This study focuses on investigating the sub-harmonic responses induced by piecewise-type nonlinearities in the middle of various dynamic behaviors in a torsional vibratory system. To examine the dynamic characteristics in a sub-harmonic regime, the harmonic balance method (HBM) was implemented. Its results were compared with the numerical simulation (NS). To reveal the sub-harmonic responses, the input conditions of the HBM were modified with a small number of input values. In addition, bifurcation diagrams were numerically determined and projected onto stable and unstable solutions of the HBM to examine the effective dynamic behaviors within the unstable regimes. The results of the HBM with the modified input conditions reveal the sub-harmonic effects well, and the comparisons of bifurcation diagrams under unstable conditions lead to an understanding of the complex dynamic behaviors. Overall, this study suggests the first analytical technique to determine the sub-harmonic responses with the HBM, and second investigates the complex dynamic behaviors in a practical vibratory system by considering the bifurcations in the unstable regimes.

By using the time-dependent hydrodynamic equations, we carry out a theoretical study of nonlinear dynamics in an n+nn+ double-layer graphene diode driven by terahertz radia-tion. A cooperative nonlinear oscillatory mode shows up due to the negative differential conductance effect. We use different chaos-detecting methods, such as the Poincaré bifurcation diagram and the first return map, to examine the transitions between the periodic and chaotic states. The double-layer graphene diode shows typical nonlinear dynamical behavior with the DC bias, AC amplitudes and the AC frequency as the control parameters.

Through analyzing the operating principles of $V^{2}$ controlled buck converters, 2-D discrete-time models and accurate switched models of $V^{2}$ controlled buck converters with trailing-edge and leading-edge modulations are established, respectively. The discrete-time models demonstrate the advantages of simple modeling and less computational complexity. Based on this, the dynamical behaviors of $V^{2}$ controlled buck converters are revealed through bifurcation diagrams and the boundary equations are derived by using the Jacobian matrix. Meanwhile, the operating regions with varying output capacitor time-constants are divided effectively by the boundary equations. The time-domain waveforms and phase portraits are also obtained through time-domain simulation. The research results indicate that trailing-edge- and leading-edge-modulated buck converters have symmetrical dynamical behaviors, such as symmetrical bifurcation, symmetrical time-domain waveforms, symmetrical phase portraits, and symmetrical period-doubling bifurcation boundaries. A symmetrical axis (SA) or a symmetrical point (SP) can be found in bifurcation diagrams, time-domain waveforms, phase portraits, and period-doubling bifurcation boundaries with varying output capacitor time-constants and duty ratios. By ramp compensation, the operating states of $V^{2}$ controlled buck converters with trailing-edge and leading-edge modulations could be effectively stabilized from unstable to stable periodic state. Experimental results are further given to verify the theoretical analysis and simulation results.

Aero-engine rotor system contains a variety of connectors such as bolts and bearings. However, the dynamic behaviors of the connection are complex in actual engineering. In this paper, the dynamic behavior of the rotor-bearing system with bolted joints and the influence of the parameters of the joints on it are clarified. The parameters include the bearing clearance and the deflection caused by the uneven bolt preload. A rotor-bearing model with bolted joints is established by using Lagrange equations. The bifurcation diagram is solved to explore the tendency of vibration of the system at different speeds by considering the Hertz contact force. Furthermore, the phase diagram, Poincaré map, time-domain steady-state response curve, and spectrum diagram are used to discuss the dynamic behaviors of the system specifically. The influence of the bearing clearance change and uneven bolt preload on the dynamic behaviors is investigated by using the bifurcation diagram. The result shows that the motion of the system is extremely complex, which includes chaotic motion. The Lyapunov exponent is then calculated to verify whether the system enters chaos. The correctness of the model is verified by comparing the result in this work with those in the literature. The model can clarify the dynamic behaviors of the system well and has high accuracy, which can provide the theoretical guidance for the design of rotor-bearing systems with bolted joints.

Bifurcation phenomena in CSTR dynamics: A system with extraneous thermal capacitance

Download options Please wait... Article information DOI https://doi.org/10.1039/P19930002969 Article type Paper Download Citation J. Chem. Soc., Perkin Trans. 1, 1993, 2969-2973 BibTex EndNote MEDLINE ProCite ReferenceManager RefWorks RIS Permissions Request permissions Chiral chlorobismuthines stabilized by the intramolecular coordination of an N,N-dimethylamino group: X-ray structure analysis, asymmetric induction at the bismuth centre, and dynamic behaviour in solution H. Suzuki, T. Murafuji, Y. Matano and N. Azuma, J. Chem. Soc., Perkin Trans. 1, 1993, 2969 DOI: 10.1039/P19930002969 To request permission to reproduce material from this article, please go to the Copyright Clearance Center request page. If you are an author contributing to an RSC publication, you do not need to request permission provided correct acknowledgement is given. If you are the author of this article, you do not need to request permission to reproduce figures and diagrams provided correct acknowledgement is given. If you want to reproduce the whole article in a third-party publication (excluding your thesis/dissertation for which permission is not required) please go to the Copyright Clearance Center request page. Read more about how to correctly acknowledge RSC content. Search articles by author Hitomi Suzuki Toshihiro Murafuji Yoshihiro Matano Nagao Azuma