No abstract is provided for this article.
No abstract is provided for this article.
This paper proves that every transformation defined on a Borel probability measure space satisfying the large deviations theorem is ergodic. As a corollary, every strongly topologically ergodic dynamical system satisfying the large deviations theorem is syndetically sensitive, improving the main result obtained by Li (2013).
No abstract is provided for this article.
In this paper we show, both analytically and experimentally, that the Rössler system synchronization is either asymptotically stable or orbitally stable within a wide range of the system key parameters. In the meantime, we provide some simple sufficient conditions for synchronization stabilities of the Rössler system in a general situation. Our computer simulation shows that the type of stability of the synchronization is very sensitive to the initial values of the two (drive and response) Rössler systems, especially for higher-periodic synchronizing trajectories, which is believed to be a fundamental characteristic of chaotic synchronization that preserves the extreme sensitivity to initial conditions of chaotic systems.
In this paper, a simple and direct statistical method is proposed for estimating the Lyapunov exponent of an unknown dynamic system using its time series of observation data. It is shown that the asymptotic distribution of the estimates obtained from the proposed method is normal. Monte Carlo and block bootstrap methods are used to simulate the estimation for the logistic map, in which they both provide the expectation and variance for the estimates. Computer simulations show that our estimates are very close to the true values of the exponent for the logistic map with different parameters.
A mathematical modeling problem for certain single flexible-link robot arms is investigated. The mathematical model proposed is based on Timoshenko's theory, with suitable initial-terminal and boundary conditions. Formulas for the kinematics (the hub angle, tip position, and deflection) and dynamics (the control torque input of the link) of the robot arm model are derived. Computer simulation results are shown and compared to some existing experimental results, confirming that the modeling of the kinematics and dynamics of the robot arm is both correct and accurate.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
Recently, synchronization of complex networks has attracted increasing attention from various research fields. However, most previous works focused on the stability of synchronization manifold. In this paper, we analyze the time-delay tolerance and converging speed of synchronization. Our theoretical analysis and extensive simulations show that the critical value of time delay for network synchronization is inversely proportional to the largest Laplacian eigenvalue, the converging speed without time delay is proportional to the second least Laplacian eigenvalue, and the time delay could increase the converging speed linearly for heterogeneous networks and significantly for homogeneous networks.
For a rotor system with bearings and step-diameter shaft in the oxygen pump of an engine, the contact between the rotor and the case is considered, and the chaotic response and bifurcation are investigated. The system is divided into elements of elastic support, shaft and disk, and based on the transfer matrix method, the motion equation of the system is derived, and solved by Newmark integration method. It is found that hardening the support can delay the occurrence of chaos. When rubbing begins, the grazing bifurcation will cause periodic motion to become quasi-period. With variation of system parameters, such as rotating speed, imbalance and external damping, chaotic response can be observed, along with other complex dynamics such as period- doubling bifurcation and torus bifurcation in the response.
We study the integrability of the Lotka–Volterra type systems with 1 : − ( 3 q − 1 ) resonances. We prove some sufficient conditions for the integrabilities of the systems and give some necessary conditions by studying the first two saddle values of the system. In the particular cases of 1 : − 2 , 1 : − 5 and 1 : − 8 resonances, we derive necessary and sufficient conditions for the integrabilities of the systems.
No abstract is provided for this article.
A harmonic oscillator with two discrete time delays is considered. The local stability of the zero solution of this equation is investigated by analyzing the corresponding transcendental characteristic equation of its linearized equation and employing the Nyquist criterion. Some general stability criteria involving the delays and the system parameters are derived. By choosing one of the delays as a bifurcation parameter, the model is found to undergo a sequence of Hopf bifurcation. The direction and stability of the bifurcating periodic solutions are determined by using the normal form theory and the center manifold theorem. Resonant codimension-two bifurcation is also found to occur in this model. A complete description is given to the location of points in the parameter space at which the transcendental characteristic equation possesses two pairs of pure imaginary roots, ±iω 1 , ±iω 2 with ω 1 :ω 2 = m:n, where m and n are positive integers. Some numerical examples are finally given for justifying the theoretical results.
This paper studies traveling wave solutions of a generalized Sasa–Satsuma equation introduced in [Adem et al., 2020]. For the cases of [Formula: see text], under given parameter conditions, the bifurcations of traveling wave solutions in the parameter space are investigated for the corresponding traveling systems. All possible explicit exact parametric representations of various solutions are obtained.
Using the dynamical systems analysis and singular traveling wave theory developed by Li and Chen [2007] to the classical and modified Serre shallow water wave equations, it is shown that, in different regions of the parameter space, all possible bounded solutions (solitary wave solutions, kink wave solutions, peakons, pseudo-peakons and periodic peakons as well as compactons) can be obtained. More than 28 explicit and exact parametric representations are precisely derived. It is demonstrated that, more interestingly, the modified Serre equation has uncountably infinitely many smooth solitary wave solutions and uncountably infinitely many pseudo-peakon solutions. Moreover, it is found that, differing from the well-known peakon solution of the Camassa–Holm equation, the modified Serre equation has four new forms of peakon solutions.
