Chaotic behaviors of the (2+1)-dimensional generalized Breor-Kaup system

With the help of the Maple symbolic computation system and the projective equation approach,a new family of variable separation solutions with arbitrary functions for the（2＋1）-dimensional generalized Breor-Kaup（GBK） system is derived.Based on the derived solitary wave solution,some chaotic behaviors of the GBK system are investigated.

On the Chaotic Behavior and Predictability of the Real Atmosphere

In this paper the concept of Chaos and its applications to the study of predictability theory is introduced. The author's attempt is to give a general overview of ideas and methods involved in this problem to scientists,who are interested in the problem of predictability but not familiar with the theory of chaos. The problem is discussed in 4 sections. In the first section, the concept of chaos and the study methods are outlined briefly; in the second section, the methods of quantitatively measuring the main characteristics of chaos which are the basis for the predictability theory are introduced; the third section discusses the time series analysis for directly studying chaotic phenomena in practical problems; and the last section presents some research results on the chaotic characteristics and the predictability of the real atmosphere.

Chaotic behavior learning of Chua's circuit

Least-square support vector machines（LS-SVM） are applied for learning the chaotic behavior of Chua＇s circuit.The system is divided into three multiple-input single-output（MISO） structures and the LS-SVM are trained individually.Comparing with classical approaches,the proposed one reduces the structural complexity and the selection of parameters is avoided.Some parameters of the attractor are used to compare the chaotic behavior of the reconstructed and the original systems for model validation.Results show that the LS-SVM combined with the MISO can be trained to identify the underlying link among Chua＇s circuit state variables,and exhibit the chaotic attractors under the autonomous working mode.

Chaos in a fractional-order micro-electro-mechanical resonator and its suppression

The present paper investigates the existence of chaos in a non-autonomous fractional-order micro-electromechanical resonator system（FOMEMRS）.Using the maximal Lyapunov exponent criterion,we show that the FOMEMRS exhibits chaos.Strange attractors of the system are plotted to validate its chaotic behavior.Afterward,a novel fractional finite-time controller is introduced to suppress the chaos of the FOMEMRS with model uncertainties and external disturbances in a given finite time.Using the latest version of the fractional Lyapunov theory,the finite time stability and robustness of the proposed scheme are proved.Finally,we present some computer simulations to illustrate the usefulness and applicability of the proposed method.

Predicting test data of aluminum honeycomb sandwich board based on volterra adaptive filters

Random vibration test was done on aluminum honeycomb sandwich board.The result suggested that chaotic behavior is found in the test data.The Volterra expression can not be gained from the input and output data directly in this paper.The state space reconstruction was used to convert the system observed data into the quasi-input/output pairs,and the second-order Volterra adaptive filter was used to predict the test data.It is shown that combining the state space reconstruction with the Volterra adaptive filter,these chaotic series could be accurately predicted.

Harmonic Mode-Locked Ytterbium-Doped Fibre Ring Laser

We demonstrate a harmonic mode-locked ytterbium-doped fibre ring laser, which consists of a polarization-sensitive isolator, two polarization controllers, two 976nm laser diodes as the pump source and a two-segment ytterbium-doped fibre. Utilizing an additive pulse mode-locked technique based on nonlinear polarization evolution, the ytterbium-doped fibre laser can operate in mode-locked state by adjusting the position of polarization controllers. The cavity fundamental repetition rate is 23.78 MHz. We also observe the second- and third-harmonic mode locking in the normal dispersion region, and their repetition rates are 47.66 MHz and 71.56 MHz, respectively. Over-driving of the saturable absorber in the harmonic mode-locking pulse is analysed and discussed in detail.

Nonlinear Dynamic Behavior of Moored Buoy Excited by Free Surface Waves

In this paper, studied are the dynamics of a moored buoy near the surface subjected to wave excitation. According to the physical structure, submersible buoy moored by tethered line is modeled firstly. Then from the differential equations, the natural frequencies are estimated by neglecting the coupling between tangential and normal direction. By use of numerical integration method, solutions are obtained. On this basis, strange attractors and bifurcation phenomena are obtained by applying Poineare map, phase plots and bifurcation diagram, showing the existence of the chaotic response in this system when wave steepness is high enough.

DETECTION OF EARLY RUB-IMPACT IN ROTORS VIA HIGHER-ORDER TIME-FREQUENCY ENTROPY

Due to the calculation problem of classical methods (such as Lyapunovexponent) for chaotic behavior, a new method of identifying nonlinear dynamics with higher-ordertime-frequency entropy (HOTFE) based on time-frequency analysis and information theorem is proposed.Firstly, the meaning of HOTFE is defined, and then its validity is testified by numericalsimulation. In the end vibration data from rotors are analyzed by HOTFE. The results demonstratethat it can indeed identify the early rub-impact chaotic behavior in rotors and also is simpler tocalculate than previous methods.

Dynamics of a Bertrand Duopoly Game of the Greek Oil Market and Application of the d-Backtest Method

This work presents the complexity that emerges in a Bertrand duopoly between two companies in the Greek oil market, one of which is semi-public and the other is private. The game uses linear demand functions for differentiated products from the existing literature and asymmetric cost functions that arose after approaches using the published financial reports of the two oil companies (Hellenic Petroleum and Motor Oil). The game is based on the assumption of homogeneous players who are characterized by bounded rationality and follow an adjustment mechanism. The players’ decisions for each time period are expressed by two difference equations. A dynamical analysis of the game’s discrete dynamical system is made by finding the equilibrium positions and studying their stability. Numerical simulations include bifurcation diagrams and strange attractors. Lyapunov numbers’ graphs and sensitivity analysis in initial conditions prove the algebraic results and reveal the complexity and chaotic behavior of the system focusing on the two parameters k1 and k2 (speed of adjustment for each player). The d-Backtest method is applied through which an attempt is made to control the chaos that appears outside the stability space in order to return to the locally asymptotically stable Nash equilibrium for the system.

Entropy Production and Fractal Dimensions in Heavy Ion Nuclear Reaction at Intermediate Energies

The characteristics of the nonlinear dynamics in the Heavy Ion Collision (HIC) at intermediate energies have been studied by evaluating the productions of the Generalized Entropy (GE) and the Multifragmentation Entropy (ME) as well as the features of the information and fractal dimensions within the Isospin Quantum Molecular Dynamical Model compensated by the lattice methods. Results demonstrate from various views that the existence of deterministic chaos in the dynamical process of reaction.

Dynamical Analysis of Rub-impact Rotor System with Asymmetric Oil Film Force

Considering the effect of non-symmetry film force, nonlinear stiffness and nonlinear friction force, a dynamical model of rub-impact rotor system is established, then the nonlinear dynamical behavior is studied by numerical analysis method. The effect of rotation speed, nonlinear stiffitess ratio and speed effect factor on brifurcation and chaotic behavior for rub-impact rotor system is comprehensively analyzed. The analysis results show that the effect of non-symmetry film force, nonlinear stiffness and nonlinear friction force on the dynamical behavior of the rotor system has close relation with rotation speed. The chaotic behavior exists in a wider parameter region, and the chaotic evolution rule is more complicated. The research provides a reliable theory basis and reference for diagnosing some faults of the rotor system.

Hopf bifurcation and chaos in a Leslie–Gower prey–predator model with discrete delays

In this work,a Leslie–Gower prey-predator model with two discrete delays has been investigated.The positivity,boundedness and persistence of the delayed system have been discussed.The system exhibits the phenomenon of Hopf bifurcation with respect to both delays.The conditions for occurrence of Hopf bifurcation are obtained for different combinations of delays.It is shown that delay induces the complexity in the system and brings the periodic oscillations,quasi-periodic oscillations and chaos.The properties of periodic solution have been determined using central manifold and normal form theory.Further,the global stability of the system has been established for different cases of discrete delays.The numerical computation has also been performed to verify analytical results.

Temporal and spatial chaos in the Kerr-AdS black hole in an extended phase space

Based on the Melnikov method,we investigate chaotic behaviors in the extended thermodynamic phase space for a slowly rotating Kerr-AdS black hole under temporal and spatial perturbations.Our results show that the temporal perturbation coming from a thermal quench of the spinodal region in the phase diagram may cause temporal chaos only when the perturbation amplitude is above a critical value,which involves the angular momentum J.Under the spatial perturbation,however,it is found that spatial chaos always occurs,independent of the perturbation amplitude.

Peak Current Control Strategy with Extended-State Tracking Compensator for DC-DC in Hybrid Energy Storage System

Because variations of ultra-capacitor voltage and battery voltage generate subharmonic and chaotic behaviors in hybrid energy storage system (HESS) application when a DC-DC converter is under the peak current control, a novel digital control strategy, i.e., peak current control with extended-state tracking compensator, is introduced to deal with the stability. The gains of the control algorithm are selected based on pole locations formulated from the Bessel filter. The simulation results validate that under the peak current control strategy with compensator, the DC-DC converter does not have the subharmonic and chaotic behaviors. The response time under the peak current control with compensator is the same as that under the peak current control. The ripple voltage and ripple current of battery are less. The tracking error of inductor current tends to zero.

Plasticity performance of Al_(0.5)CoCrCuFeNi high-entropy alloys under nanoindentation

The statistical and dynamic behaviors of the displacement-load curves of a high-entropy alloy,Al_（0.5）CoCrCuFeNi,were analyzed for the nanoindentation performed at two temperatures.Critical behavior of serrations at room temperature and chaotic flows at 200°C were detected.These results are attributed to the interaction among a large number of slip bands.For the nanoindentation at room temperature,recurrent partial events between slip bands introduce a hierarchy of length scales,leading to a critical state.For the nanoindentation at 200°C,there is no spatial interference between two slip bands,which is corresponding to the evolution of separated trajectory of chaotic behavior.