Hyperchaos--chaos--Hyperchaos Transition in a Class of On--Off Intermittent Systems Driven by a Family of Generalized Lorenz Systems

Blowout bifurcation in nonlinear systems occurs when a chaotic attractor lying in some symmetric subspace becomes transversely unstable. A class of five-dimensional continuous autonomous systems is considered, in which a two-dimensional subsystem is driven by a family of generalized Lorenz systems. The systems have some common dynamical characters. As the coupling parameter changes, blowout bifurcations occur in these systems and brings on change of the systems＇ dynamics. After the bifurcation the phenomenon of on-off intermittency appears. It is observed that the systems undergo a symmetric hyperchaos-chaos-hyperchaos transition via or after blowout bifurcations. An example of the systems is given, in which the drive system is the Chen system. We investigate the dynamical behaviour before and after the blowout bifurcation in the systems and make an analysis of the transition process. It is shown that in such coupled chaotic continuous systems, blowout bifurcation leads to a transition from chaos to hyperchaos for the whole systems, which provides a route to hyperchaos.     

Type II quantum chaos

A classification of quantum systems into three categories, type I, II and III, is proposed. The classification is based on the degree of sensitivity upon initial conditions, and the appearance of chaos. The quantum dynamics of type I systems is quasi periodic displaying no exponential sensitivity. They arise, e.g., as the quantized versions of classical chaotic systems. Type II systems are obtained when classical and quantum degrees of freedom are coupled. Such systems arise naturally in a dynamic extension of the first step of the Born-Oppenheimer approximation, and are of particular importance to molecular and solid state physics. Type II systems can show exponential sensitivity in the quantum subsystem. Type III systems are fully quantized systems which show exponential sensitivity in the quantum dynamics. No example of a type III system is currently established. This paper presents a detailed discussion of a type II quantum chaotic system which models a coupled electronic-vibronic system. It is argued that type II systems are of importance for any field systems (not necessarily quantum) that couple to classical degrees of freedom.     

Stationary solutions of Liouville equations for non-Hamiltonian systems

We consider the class of non-Hamiltonian and dissipative statistical systems with distributions that are determined by the Hamiltonian. The distributions are derived analytically as stationary solutions of the Liouville equation for non-Hamiltonian systems. The class of non-Hamiltonian systems can be described by a non-holonomic (non-integrable) constraint: the velocity of the elementary phase volume change is directly proportional to the power of non-potential forces. The coefficient of this proportionality is determined by Hamiltonian. The constant temperature systems, canonical-dissipative systems, and Fermi-Bose classical systems are the special cases of this class of non-Hamiltonian systems.     

Dynamics of Hamiltonian systems under piecewise linear forcing

A two-parameter family of smooth Hamiltonian systems perturbed by a piecewise linear force is analyzed. The systems are represented both as maps and as dynamical systems. Currently available analytical and numerical results concerning the onset of chaos and global diffusion in such systems are reviewed. Dynamical behavior that has no analogs in the class of systems with analytic Hamiltonians is described. A comparison with the well-studied dynamics of a driven pendulum is presented, and essential differences in dynamics between smooth and analytic systems are highlighted.     

Complex pole approach in thermodynamic description of fluid mixtures with small number of molecules

The subject matter of classical thermodynamics is the asymptotic behavior of equilibrium systems in thermodynamic limit, for small molecular systems, when transition to thermodynamic limit is impossible, the extension of thermodynamics is required. This work studies novel approach for the evaluation of partition functions of small systems by complex pole analysis. Several cases for molecular systems in small cavities are studied numerically. In particular size-dependent additional pressure for small systems is evaluated analytically and numerically. Similar approach was developed earlier in nuclear physics for finite systems of nucleons. The obtained results correspond to published experimental data and molecular dynamics simulations.     

On Chaotification of Discrete Lagrange Systems

This paper is concerned with chaotification of discrete Lagrange systems in one dimension, via feedback control techniques. A chaotification theorem for discrete Lagrange systems is established. The controlled systems are proved to be chaotic in the sense of Devaney. In particular, the systems corresponding to the original systems and designed controllers are only required to satisfy some mild assumptions.     

Measure Synchronization on Symplectic Map

Measure synchronization in coupled Hamiltonian systems is a novel synchronization phenomenon. The measure synchronization on symplectic map is observed numerically, for identical coupled systems with different parameters. We have found the properties of the characteristic frequency and the amplitude of phase locking in regular motion when the measure synchronization of coupled systems is obtained. The relations between the change of the largest Lyapunov exponent and the course of phase desynchronization are also discussed in coupled systems, some useful results are obtained. A new approach is proposed for describing the measure synchronization of coupled systems numerically, which is advantage in judging the measure synchronization, especially for the coupled systems in nonregular region.     

一种分数阶混沌系统同步的自适应滑模控制器设计

针对分数阶混沌系统的同步问题, 基于滑模控制理论和自适应控制理论, 设计了一个具有较强鲁棒性的分数阶积分滑模面, 并提出了一种自适应滑模控制器在不消除非线性项的情况下实现一类三维分数阶混沌系统同步的方法. 利用所设计的自适应滑膜控制器实现了分数阶Chen系统、分数阶Liu系统以及分数阶Arneodo系统的混沌同步. 数值模拟仿真结果验证了所设计的控制器的有效性和可行性.     

Multistability in coupled different-dimensional dynamical systems

Multistability or coexistence of different chaotic attractors for a given set of parameters depending on the initial condition only is one of the most exciting phenomenon in dynamical systems. The schemes to design multistability systems via coupling two identical or non-identical but the same-dimensional systems have been proposed earlier. Coupled different-dimensional systems are very useful to describe the real-world physical and biological systems. In this paper, a scheme for designing a multistable system by coupling two different-dimensional dynamical systems has been proposed. Coupled Lorenz and Lorenz–Stenflo systems have been considered to illustrate the scheme. The efficiency of the scheme is shown numerically, by presenting phase diagrams, bifurcation diagrams and variation of maximum Lyapunov exponents.     

Detection and Characterization of Membrane Microheterogeneity by Resonance Energy Transfer

The application of resonance energy transfer (RET) in the study of heterogeneity in membrane systems is described. Useful formalisms for monophasic and biphasic systems are presented, together with quantitative studies. Evidence for reduction of dimensionality, probe segregation, and microdomain sizes in these systems is discussed. Selected examples of multicomponent systems (natural membranes or model systems including proteins) are also referred, as well as recent work using RET under the microscope.     

一种参数摄动的混沌异结构同步方法

研究了参数摄动情形下的混沌异结构同步问题,基于Lyapunov稳定性定理并结合范数理论给出了系统参数摄动下实现混沌异结构同步的一个充分条件,为同步控制器的设计提供了一般方法.只要两混沌系统维数相等,状态变量可测,就可利用所提方法实现系统参数摄动下的异结构同步,并能够保证在同步实现后同步控制量伴随误差变量一同收敛至零.该方法鲁棒性强,适用范围广,通过对混沌系统、超混沌系统的同步仿真,证实了该方法的有效性. 关键词： 混沌 超混沌 同步 Lyapunov函数     

Integrating Factors and Conservation Laws for Relativistic Mechanical System

In this paper, we present a new method to construct the conservation laws for relativistic mechanical systems by finding corresponding integrating factors. First, the Lagrange equations of relativisticmechanical systems are established, and the definition of integrating factors of the systems is given; second, the necessary conditions for the existence of conserved quantities of the relativistic mechanical systems are studied in detail, and the relation between the conservation laws and the integrating factors of the systems is obtained and the generaized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the systems are established, and an example is given to illustrate the application of the results.     

Integrating Factors and Conservation Laws for Relativistic Mechanical System

In this paper, we present a new method to construct the conservation laws for relativistic mechanical systems by finding corresponding integrating factors. First, the Lagrange equations of relativistic mechanical systems are established, and the definition of integrating factors of the systems is given; second, the necessary conditions for the existence of conserved quantities of the relativistic mechanical systems are studied in detail, and the relation between the conservation laws and the integrating factors of the systems is obtained and the generalized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the systems are established, and an example is given to illustrate the application of the results.     

Construction of Exact Invariants for Time Dependent Classical Dynamical Systems

In the present work, we survey various methodsused for the construction of exact invariants fordynamical systems involving an explicit time dependence.More stress is placed on two-dimensional (2D) than one-dimensional (1D) systems. While bothharmonic and anharmonic time-dependent (TD) systems arediscussed in the 1D case, the construction of invariantsis carried out for several interesting central and noncentral systems in 2D. The method ofcomplexification of two space dimensions is described indetail. The TD coupled oscillator problem, which in analternative form suggests the generalization of Ermakov systems, is analyzed in greater detail. Theavailable methods in the 2D case provide only the firstinvariant, and that for a few TD systems. These methodsas such are still inadequate as far as the construction of the second invariant is concerned. The roleand scope of some of the derived invariants in thecontext of various physical problems are highlighted.The possibility of extension of some of these methods to 3D TD systems is also discussed.     

Consensus of compound-order multi-agent systems with communication delays

In complex environments, many distributed networked systems can only be illustrated with fractional-order dynamics. When multi-agent systems show individual diversity with difference agents, heterogeneous (integer-order and fractional-order) dynamics are used to illustrate the agent systems and compose integerfractional compounded-order systems. Applying Laplace transform and frequency domain theory of the fractional-order operator, the consensus of delayed multi-agent systems with directed weighted topologies is studied. Since an integer-order model is the special case of a fractional-order model, the results in this paper can be extended to systems with integer-order models. Finally, numerical examples are used to verify our results.     

Tri-polarized MIMO systems in real-world channels: Channel investigation and performance analysis

Polarized multi-antenna systems are an effective solution for reducing inter-antenna spacing while still maintaining low inter-antenna correlation. Traditionally, only dual-polarized antenna systems are used for polarized transceivers. In this paper, tri-polarized antenna systems are investigated. Starting from the polarization mechanisms in the wireless propagation channel, it is shown that dual-polarized MIMO systems show high sensitivity to the transmitter and receiver orientation, which may be very critical in practical applications. Tri-polarized MIMO systems are introduced as a solution to obtain a robust MIMO performances, which are independent of the transmitter and receiver orientation. The performances of dual- and tri-polarized MIMO systems are evaluated on real-world measured channels, and the limits of each of these systems is highlighted.     

Conductance and conductance fluctuations of mesoscopic systems with different symmetries: a statistical scattering theory approach

A theoretical model of mesoscopic systems, recently introduced by Iida et al. (IWZ), is extended to the case of systems with spin dependent interactions and systems of broken time reversal invariance. The quantum mechanical time reversal operator is represented by an operator acting in a space of abstract matrix fields. Thereby, the discussion of systems with different time reversal behaviour can be unified almost entirely. We recast the IWZ-model in a new parametrization, which is more closely related to other field theoretic models of mesoscopic systems, than the original one.     

Chaotification of discrete dynamical systems via impulsive control

This Letter is concerned with chaotification of discrete dynamical systems in finite-dimensional real spaces, via impulsive control techniques. Chaotification theorems for one-dimensional discrete dynamical systems and general higher-dimensional discrete dynamical systems are derived, respectively, whether the original systems are stable or not. Finally, the effectiveness of the theoretical results is illustrated by some numerical examples.     

Heisenberg’s Uncertainty Relation and Bell Inequalities in High Energy Physics

An effective formalism is developed to handle decaying two-state systems. Herewith, observables of such systems can be described by a single operator in the Heisenberg picture. This allows for using the usual framework in quantum information theory and, hence, to enlighten the quantum features of such systems compared to non-decaying systems. We apply it to systems in high energy physics, i.e. to oscillating meson–antimeson systems. In particular, we discuss the entropic Heisenberg uncertainty relation for observables measured at different times at accelerator facilities including the effect of CP\mathcal{CP} violation, i.e. the imbalance of matter and antimatter. An operator-form of Bell inequalities for systems in high energy physics is presented, i.e. a Bell-witness operator, which allows for simple analysis of unstable systems.