Equilibrium points and bifurcation control of a chaotic system

Based on the Routh-Hurwitz criterion, this paper investigates the stability of a new chaotic system. State feedback controllers are designed to control the chaotic system to the unsteady equilibrium points and limit cycle. Theoretical analyses give the range of value of control parameters to stabilize the unsteady equilibrium points of the chaotic system and its critical parameter for generating Hopf bifurcation. Certain nP periodic orbits can be stabilized by parameter adjustment. Numerical simulations indicate that the method can effectively guide the system trajectories to unsteady equilibrium points and periodic orbits.     

A novel one equilibrium hyper-chaotic system generated upon Lü attractor

By introducing an additional state feedback into a three-dimensional autonomous chaotic attractor Lü system, this paper presents a novel four-dimensional continuous autonomous hyper-chaotic system which has only one equilibrium. There are only 8 terms in all four equations of the new hyper-chaotic system, which may be less than any other four-dimensional continuous autonomous hyper-chaotic systems generated by three-dimensional (3D) continuous autonomous chaotic systems. The hyper-chaotic system undergoes Hopf bifurcation when parameter c varies, and becomes the 3D modified Lü system when parameter k varies. Although the hyper-chaotic system does not undergo Hopf bifurcation when parameter k varies, many dynamic behaviours such as periodic attractor, quasi periodic attractor, chaotic attractor and hyper-chaotic attractor can be observed. A circuit is also designed when parameter k varies and the results of the circuit experiment are in good agreement with those of simulation.     

Finite-time Mittag—Leffler synchronization of fractional-order complex-valued memristive neural networks with time delay

Without dividing the complex-valued systems into two real-valued ones, a class of fractional-order complex-valued memristive neural networks (FCVMNNs) with time delay is investigated. Firstly, based on the complex-valued sign function, a novel complex-valued feedback controller is devised to research such systems. Under the framework of Filippov solution, differential inclusion theory and Lyapunov stability theorem, the finite-time Mittag—Leffler synchronization (FTMLS) of FCVMNNs with time delay can be realized. Meanwhile, the upper bound of the synchronization settling time (SST) is less conservative than previous results. In addition, by adjusting controller parameters, the global asymptotic synchronization of FCVMNNs with time delay can also be realized, which improves and enrich some existing results. Lastly, some simulation examples are designed to verify the validity of conclusions.     

A novel resource management scheme for virtualized cyber–physical–social system

Cyber–physical–social systems (CPSSs) can realize the coordination of the physical world, cyber space, and society. This article presents a virtualized CPSS architecture with a user incentive scheme. The proposal supports the dimension-extended resource management for virtualized CPSSs, where humans are viewed as an additional network resource to be jointly optimized with other resources, i.e., communication, caching, and computing resources. The proposal aims at maximizing the profit of the virtual CPSS operator based on the average spectrum efficiency and user reputation and capability evaluation. Simulation results indicate that the proposal can fully mobilize high-quality users and meanwhile provide superior services to them; thus it can motivate humans to regularize or modify their behaviors in the direction of improvement in overall revenue.     

A novel symbol overlapping FFH-OCDMA system

Anovel symbol overlapping optical fast frequency-hop code-division multiple access(FFH-OCDMA)system is proposed, and its bit error rate(BER) performance is investigated under consideration of avalanche photonic diode(APD) noise and thermal noise. An esperimental symbol overlapping(SO)FFH-OCDMA testbed is developed and some experimental results are given. The theoretical and experimental results show that the system is apt to implement and has larger throughput.     

Dynamics of a new composite four–Scroll chaotic system

A new three-dimensional autonomous chaotic system is proposed. This new system can generate single-scroll, double-scroll, three-scroll and four-scroll attractors under different system parameters. Particularly, it can generate a four-scroll chaotic attractor composed of a large Chua-like attractor and a small Lorenz-like attractor. And the system can also generate a nested three-scroll attractor and the multi-double-scroll chaotic attractor. In addition, the system possesses the chaotic state transition, and the number of scrolls will change in the state transition process. The formation mechanism of the composite four-scroll chaotic attractor is analyzed in detail. The dynamic analysis methods include time series, 0–1 test chart, phase diagram, bifurcation diagram and Lyapunov exponents are used to describe some basic dynamics behaviors of the proposed system.     

A lattice Maxwell system with discrete space–time symmetry and local energy–momentum conservation

A lattice Maxwell system is developed with gauge-symmetry, symplectic structure and discrete space–time symmetry. Noether's theorem for Lie group symmetries is generalized to discrete group symmetries for the lattice Maxwell system. As a result, the lattice Maxwell system is shown to admit a discrete local energy–momentum conservation law corresponding to the discrete space–time symmetry. A lattice model that respects all local conservation laws and geometric structures is as good as and probably more preferable than standard models on continuous space–time. It can also be viewed as an effective algorithm for the governing differential equations on continuous space–time.     

Synchronization of the time—varying parameter chaotic system and its application to secure communication

In this paper we propose and investigate the synchronization of a new chaotic model with time-varying parameters and apply it to improve the security of chaotic communication. In this model, the chaotic system is modulated by both the message and the varying parameters. The varying parameters distort the phase space so heavily that they prevent the carrier from being broken by nonlinear dynamic forecasting method. Theory and simulation experiments with speech signal communication indicate that the receiver can gain a perfect synchronization with the transmitter, and the intruder cannot break down this communication system. We also discuss the robustness of the new communication system.     

A study on pattern time delay shift coding underwater acoustic communication

1IntroductionWiththestimulusofmarket,techniquesofradiocommunication,satellitecommunication,optical-fibercommunicationandmovablecommunicationarerapidlydeveloped,butunderwaterdigitalcommunicationviaacousticwaveisanewdevelopingtechnique.Therearemanypublishedliteraturesonunderwateracousticcommunicationll]-l21].Thehighspeedunderwateracousticcommunicationtechniqueforverticalchannelindeepwaterismoredeveloped,butitisnotsatisfiedforhorizontalchannelbecauseofthelimitationofmultipath.Inhorizontalchannel,…     

A reliable analytical algorithm for space–time fractional cubic isothermal autocatalytic chemical system

The nucleus-acoustic shock waves (NASWs) propagating in a white dwarf plasma system, which contain non-relativistically or ultrarelativistically degenerate electrons, non-relativistically degenerate, viscous fluid of light nuclei, and immobile nuclei of heavy elements, have been theoretically investigated. We have used the reductive perturbation method, which is valid for small but finite-amplitude NASWs to derive the Burgers equation. The NASWs are, in fact, associated with the nucleus-acoustic (NA) waves in which the inertia is provided by the light nuclei, and restoring force is provided by the degenerate pressure of electrons. On the other hand, the stationary heavy nuclei participate only in maintaining the background charge neutrality condition at equilibrium. It is found that the viscous force acting in the fluid of light nuclei is a source of dissipation, and is responsible for the formation of NASWs. It is also observed that the basic features (polarity, amplitude, width, etc.) of the NASWs are significantly modified by the presence of heavy nuclei, and that NASWs are formed with either positive or negative potential depending on the values of the charge density of the heavy nuclei. The basic properties are also found to be significantly modified by the effects of ultrarelativistically degenerate electrons. The implications of our results in white dwarfs are briefly discussed.     

A novel analytical model for intensity modulated and direct detected multiple-input–multiple-output system with time related zero forcing equalization over multimode fiber

In this paper, basing on tap delay lines filter model and model spatial coupling theory, we build up a novel analytical model for an intensity modulated and direct detected multiple-input–multiple-output (IM-DDMIMO) system over multimode fiber. At the receiver side, time related zero forcing (ZF) equalization was used to recover signals. With this model, we theoretically and by simulation analyzed a 2 × 2 multimode fiber MIMO system utilizing offset launching scheme. It's found that two received streams can be well recovered by equalization. Compared with traditional single-input–single-output (SISO) system, such 2 × 2MIMO system can provide at least 5 dB Bit error rate (BER) performance improvement.     

Two triple points in the H2O–H2 system

Using a volumetric technique, phase transitions in the H₂O–H₂ system were investigated in the vicinity of two points of an invariant equilibrium, L+I _h+sII and L+sII+C ₁, located at 1.07 kbar and?10 °C and at 3.6 kbar and 1 °C, respectively. Liquid water (L), low-pressure hexagonal ice (I _h) and high-pressure cubic (sII) and rhombohedral (C ₁) clathrate hydrates were in equilibrium with gaseous hydrogen taken in excess.     

A novel MMI–MZ all-optical switch

This paper presents a novel all-optical switch based on multi-mode interference (MMI) and Mach–Zehnder (MZ) using self-imaging principle and optical Kerr effect of organic polymer material. A branch waveguide is inserted into one of Mach–Zehnder interferometer arms, where the controlling beam is introduced. The device with a core of azo polymer is simulated by the beam propagation method (BPM). The result shows that, the bent branch waveguide of 2 μm width is inserted in MZ interferometer arm at 100 μm has the minimal impact on the original waveguide. And a good light switching function is achieved via controlling light intensity of 4 mW.     

A novel formulation of Cabibbo–Kobayashi–Maskawa matrix renormalization

We present a gauge-independent quark mass counterterm for the on-shell renormalization of the Cabibbo–Kobayashi–Maskawa (CKM) matrix in the Standard Model that is directly expressed in terms of the Lorentz-invariant self-energy functions, and automatically satisfies the hermiticity constraints of the mass matrix. It is very convenient for practical applications and leads to a gauge-independent CKM counterterm matrix that preserves unitarity and satisfies other highly desirable theoretical properties, such as flavor democracy.     

Weak-noise solution of Fokker–Planck equations with n (>2) variables: A simpler evaluation near equilibrium points

A recent approach to the quasipotential of drift–diffusion models is extended to the case of n>2$n>2$ variables. The quasipotential determines the stationary probability density at weak noise, for some models even with each noise. At equilibrium points, the symmetric n-by-n matrix of its second derivatives is determined by a quadratic (Riccati) equation, and this is now replaced by a linear equation for an antisymmetric matrix of the same size. The resulting density function is unique and smooth near equilibrium points, including when the next term in the noise strength is taken into account.     

Quantum Fisher information of a qubit-qutrit system in Garfinkle–Horowitz–Strominger dilation space–time

We investigate the quantum Fisher information(QFI) of a qubit-qutrit system in the background of Garfinkle–Horowitz–Strominger dilation black hole. After deriving the analytical expression of the QFI, we examine its dynamics with respect to the dilation parameter D and the state parameter γ of the system. Our results show that the QFI for the estimation of γ is a fixed value,which is independent of the parameters D and γ. And the QFI for the estimation of D varies with the parameters D and γ. Additionally, we propose an effective strategy to steer the QFI by introducing weak measurement reversal. We find that the QFI can be remarkably enhanced by adjusting the appropriate reversing measurement strengths. Our findings might provide some useful insights for the study on parameter estimation of hybrid systems in the framework of relativity theory.     

A novel scheme based on minimum delay at the edges for optical burst switching networks

This paper proposes a novel scheme based on minimum delay at the edges (MDE) for optical burst switching (OBS) networks. This scheme is designed to overcome the long delay at the edge nodes of OBS networks. The MDE scheme features simultaneous burst assembly, channel scheduling, and pre-transmission of control packet. It also features estimated setup and explicit release (ESXR) signaling protocol. The MDE scheme can minimize the delay at the edge nodes for data packets, and improve the end-to-end latency performance for OBS networks. In addition, comparing with the conventional scheme, the performances of the MDE scheme are analyzed in this paper.     

A novel polarization modulator for a moiré system with grating imaging

Displacement measurements and position sensing have been playing an important role in many fields such as fabrication, biophysics, and autocontrol. Interferome- try, laser triangulation, optical fiber sensing and moiré technique are common optical measuring methods[1-3]. Among these methods, moiré technique holds the most interest due to its high accuracy, large range, low cost, and other advantages. When a long working distance is required, or when space is not at a premium, a moiré sys- t…