Dynamics,circuit realization,control and synchronization of a hyperchaotic hyperjerk system with coexisting attractors

Although different hyperjerk systems have been discovered, a few hyperjerk systems can exhibit hyperchaotic behavior. In this work, we introduce a new hyperjerk system with hyperchaotic attractors. By investigating dynamics of the system, we have observed the different coexisting attractors such as coexistence of period-2 attractors, or coexistence of period-2 attractor and quasiperiodic attractor. It is worth noting that this striking phenomenon is rarely reported in a hyperjerk system. The proposed system has been realized with electronic components. The agreement between the simulation and experimental results indicates the feasibility of the hyperjerk system. Moreover, chaos control and synchronization of such hyperjerk system have been also reported.     

Finding attractors of continuous-time systems by parameter switching

The review presents a parameter switching algorithm and his applications which allows numerical approximation of any attractor of a class of continuous-time dynamical systems depending linearly on a real parameter. The considered classes of systems are modeled by a general initial value problem which embeds dynamical systems continuous and discontinuous with respect to the state variable, of integer, and fractional order. The numerous results, presented in several papers, are systematized here on four representative known examples representing the four classes. The analytical proof of the algorithm convergence for the systems belonging to the continuous class is presented briefly, while for the other categories of systems, the convergence is numerically verified via computational tools. The utilized numerical tools necessary to apply the algorithm are contained in Appendices A, B, C, D and E.     

Initial offset boosting coexisting attractors in memristive multi-double-scroll Hopfield neural network

Nonlinear Dynamics - Memristors are widely considered to be promising candidates to mimic biological synapses. In this paper, by introducing a non-ideal flux-controlled memristor model into a...     

Chaos-based application of a novel no-equilibrium chaotic system with coexisting attractors

Nonlinear Dynamics - Novel chaotic system designs and their engineering applications have received considerable critical attention. In this paper, a new three-dimensional chaotic system and its...     

Numerical analyses and experimental validations of coexisting multiple attractors in Hopfield neural network

In this paper, a finite-time controller is proposed for the quadrotor aircraft to achieve hovering control in a finite time. The design of controller is mainly divided into two steps. Firstly, a saturated finite-time position controller is designed such that the position of quadrotor aircraft can reach any desired position in a finite time. Secondly, a finite-time attitude tracking controller is designed, which can guarantee that the attitude of quadrotor aircraft converges to the desired attitude in a finite time. By homogenous system theory and Lyapunov theory, the finite-time stability of the closed-loop systems is given through rigorous mathematical proofs. Finally, numerical simulations are given to show that the proposed algorithm has a faster convergence performance and a stronger disturbance rejection performance by comparing to the PD control algorithm.     

Impulsive control of chaotic attractors in nonlinear chaotic systems

Based on the study from both domestic and abroad, an impulsive control scheme on chaotic attractors in one kind of chaotic system is presented. By applying impulsive control theory of the universal equation, the asymptotically stable condition of impulsive control on chaotic attractors in such kind of nonlinear chaotic system has been deduced, andwith it, the upper bond of the impulse interval for asymptotically stable control was given.Numerical results are presented, which are considered with important reference value for control of chaotic attractors.     

Global dynamics of Chua Corsage Memristor circuit family: fixed-point loci,Hopf bifurcation,and coexisting dynamic attractors

Nonlinear Dynamics - This paper presents an in-depth and rigorous mathematical analysis of a family of nonlinear dynamical circuits whose only nonlinear component is a Chua Corsage Memristor (CCM)...     

Hyperchaotic memristive system with hidden attractors and its adaptive control scheme

In this research work a novel 4-D memristive system is presented. The proposed system belongs to the category of dynamical systems with hidden attractors as it displays a line of equilibrium points. Also, it has an hyperchaotic dynamical behavior in a particular range of its parameters space. System’s behavior is investigated through numerical simulations, by using well-known tools of nonlinear theory, such as phase portrait, bifurcation diagram, Lyapunov exponents and Poincaré map. Next, the case of chaos control of the system with unknown parameters using adaptive control method is investigated. Finally, an electronic circuit realization of the novel hyperchaotic system using Spice is presented in detail to confirm the feasibility of the theoretical model.     

Random attractors

In this paper, we generalize the notion of an attractor for the stochastic dynamical system introduced in [7]. We prove that the stochastic attractor satisfies most of the properties satisfied by the usual attractor in the theory of deterministic dynamical systems. We also show that our results apply to the stochastic Navier-Stokes equation, the white noise-driven Burgers equation, and a nonlinear stochastic wave equation.     

一种半球谐振陀螺振幅控制方法

振幅控制是半球谐振陀螺正常工作的基础,同时振幅控制的稳定性也直接影响陀螺的性能指标.针对半球谐振陀螺振幅控制问题开展研究.首先,推导了驱动力与陀螺振动幅度的传递函数,建立了振幅控制的被控对象模型;其次,提出了一种半球谐振陀螺的起振方法;然后根据已有研究设计了一种半球谐振陀螺振幅控制回路方案,并推导出振幅控制回路的闭环传...     

Convergence of attractors

I.IntroductionConsidersystemofcoupledoscillatorsi~Ax j(x)(l.;l)inwhichx~(xl,x',..',x")CRe(m>3),Aisnlxinmatrix,fisanonlinearmapfromR-toRewithconstantb>0.(l.l)isdiscretizedbyone-stepmethod:xo I~x. h(Ax" j(x.))(l'2)withconstantstepsizeh>0.LetF4denotethemapfr…     

Selection of multi-scroll attractors in Jerk circuits and their verification using Pspice

In this paper, a feasible feedback scheme is used to stabilize the multi-scroll attractors in the Jerk circuit, and the controller is realized using mixed Heaviside function. It is found that arbitrary number ( $n=2, 3, 4, 5,{\ldots }$ ) of multi-scroll attractors can be selected from a controlled Jerk circuit, and these multi-scroll attractors can be reproduced using Pspice. The implementation of circuit and controller using Pspice is also presented. The potential mechanism could be that an external forcing in the Sine type is practical to generate a group of equilibrium points, and a linear controller composed of Heaviside function is effective to stabilize the $n$ -scroll attractors in the chaotic systems.     

Attitude tracking control of flexible spacecraft with large amplitude slosh

This paper is focused on attitude tracking control of a spacecraft that is equipped with flexible appendage and partially filled liquid propellant tank. The large amplitude liquid slosh is included by using a moving pulsating ball model that is further improved to estimate the settling location of liquid in microgravity or a zero-g environment. The flexible appendage is modelled as a three-dimensional Bernoulli–Euler beam, and the assumed modal method is employed.A hybrid controller that combines sliding mode control with an adaptive algorithm is designed for spacecraft to perform attitude tracking. The proposed controller has proved to be asymptotically stable. A nonlinear model for the overall coupled system including spacecraft attitude dynamics,liquid slosh, structural vibration and control action is established. Numerical simulation results are presented to show the dynamic behaviors of the coupled system and to verify the effectiveness of the control approach when the spacecraft undergoes the disturbance produced by large amplitude slosh and appendage vibration. Lastly, the designed adaptive algorithm is found to be effective to improve the precision of attitude tracking.     

Symmetry groups of attractors

For maps equivariant under the action of a finite group on ⁿ, the possible symmetries of fixed points are known and correspond to the isotropy subgroups. This paper investigates the possible symmetries of arbitrary, possibly chaotic, attractors and finds that the necessary conditions of Melbourne, Dellnitz & Golubitsky [15] are sufficient, at least for continuous maps.This result shows that the reflection hyperplanes are important in determining those groups which are admissible; more precisely, a subgroup of is admissible as the symmetry group of an attractor if there exists a with / cyclic such that fixes a connected component of the complement of the set of reflection hyperplanes of reflections in but not in . For finite reflection groups this condition on reduces to the condition that is an isotropy subgroup. Our results are illustrated for finite subgroups of O(3).     

The structure of symmetric attractors

We consider discrete equivariant dynamical systems and obtain results about the structure of attractors for such systems. We show, for example, that the symmetry of an attractor cannot, in general, be an arbitrary subgroup of the group of symmetries. In addition, there are group-theoretic restrictions on the symmetry of connected components of a symmetric attractor. The symmetry of attractors has implications for a new type of pattern formation mechanism by which patterns appear in the time-average of a chaotic dynamical system.Our methods are topological in nature and exploit connectedness properties of the ambient space. In particular, we prove a general lemma about connected components of the complement of preimage sets and how they are permuted by the mapping.These methods do not themselves depend on equivariance. For example, we use them to prove that the presence of periodic points in the dynamics limits the number of connected components of an attractor, and, for one-dimensional mappings, to prove results on sensitive dependence and the density of periodic points.     

Transitions between two pictorial attractors

Two experiments exploring similarity judgments on pairs and triplets of stimuli drawn from pictorial series are described. The stimuli are the Man-Woman and Gypsy-Girl pictures that slowly change from one prototype to the other as one progresses along the series. These have been used previously to demonstrate hysteresis of category judgments on ambiguous figures; the Man Woman series has been both modelled as a problem in neural network theory and mapped onto part of a cusp catastrophe surface. It. is shown that the transition process is complicated with a zone of uncertainty and prevalence of bimodality in many of the pairwise similarity judgments. The dynamics are interpreted in terms of transitions between two saddle-node attractors that are themselves not a discrete pair but have some overlap in their composition.     

Large amplitude free flexural vibration of rings using finite element approach

Here, the large amplitude free flexural vibrations of isotropic/laminated orthotropic rings are investigated, using a shear flexible curved beam element based on field consistency principle. A laminated refined beam theory is introduced for developing the element, which satisfies the interface transverse shear stress and displacement continuity, and has a vanishing shear stress on the inner and outer surfaces of the beam. The formulation includes in-plane and rotary inertia effects, and the non-linearity due to the finite deformation of the ring. The governing equations obtained using Lagrange's equations of motion are solved through the direct integration technique. Amplitude-frequency relationships evaluated from the dynamic response history are examined. Detailed numerical results are presented considering various parameters such as radius-to-thickness ratio, circumferential wave number and ovality for isotropic and laminated orthotropic rings. The nature and degree of the participation of various modes in non-linear asymmetric vibration of oval ring brought out through the present study are useful for accurate modelling of the closed non-circular structures.     

Effects of T-S wave amplitude on the control of boundary layer transition bystreaks

The effects of streaks on boundary layer transition depend on the initial amplitude of T-S waves introducedto excite the transition. This problem was studied in a flat-plate boundary layer in water tunnel byusing hydrogen bubble method. Three T-S wave initial amplitudes were tested. The results show thatboth narrow and wide-spacing streaks depress the transition excited by T-S waves with lower initialamplitude. However, when transition is excited by T-S waves of higher initial amplitude, thenarrow-spacing streaks depress the transition, while the wide-spacing streaks promote thetransition. Further the underlying mechanisms were also analyzed.     

Finding the buckling load of non-uniform columns using the iteration perturbation method

The aim of this study is to calculate the critical load of variable inertia columns. The example studied in this paper can be used as a paradigm for other non-uniform columns. The wavelength of equivalent vibratory system is used to calculate the critical load of the trigonometrically varied inertia column. In doing so, the equilibrium equation of the column is theoretically studied using the perturbation method. Accuracy of the calculated results is evaluated by comparing the solution with numerical results. Effect of improving the initial guess on the solution accuracy is investigated. Effects of varying parameters of the trigonometrically varied inertia and the uniformly tapered columns on their stability behavior are studied. Finally, using the so-called “perfectibility” parameter, two design goals, i.e., being lightweight and being strong, are studied for the discussed columns.