Analytical results on the magnetization of the Hamiltonian Mean-Field model

The violent relaxation and the metastable states of the Hamiltonian Mean-Field model, a paradigmatic system of long-range interactions, is studied using a Hamiltonian formalism. Rigorous results are derived algebraically for the time evolution of selected macroscopic observables, e.g., the global magnetization. The high- and low-energy limits are investigated and the analytical predictions are compared with direct N-body simulations. The method we use enables us to re-interpret the out-of-equilibrium phase transition separating magnetized and (almost) unmagnetized regimes.     

Unstable manifolds for the hyperchaotic Rössler system

We analyse stability of the generalized four-variable Rössler oscillating system depending on selected control parameters, by using analytic and Hurwitz-Routh methods. In contrast to the usual three-dimensional Rössler and Lorenz systems, we show that always there exists at least one unstable direction, and the number of positive local Lyapunov exponents may be different for both fixed points. We have found two new types of Hopf bifurcation, in which the dimension of the unstable manifold can be increased or reduced by two. Hence there are many possibilities for hyperchaotic unstable manifolds of various dimensions. We have also calculated various ranges of the control parameters for which different unstable manifolds can be obtained. This allows a better characterization of stability of the attractors in the hyperchaotic regime.     

Chaos Behaviour of Molecular Orbit

Based on Hfickel＇s molecular orbit theory, the chaos and bifurcation behaviour of a molecular orbit modelled by a nonfinear dynamic system is studied. The relationship between molecular orbit and its energy level in the nonlinear dynamic system is obtained.     

The boundary-induced spiral wave drift in the complex Ginzburg–Landau equation

We numerically investigate the boundary-induced spiral wave drift in the complex Ginzburg–Landau equation. We find some novel phenomena for the spiral drifting dynamics such as the chaotic behaviors, the transient chaos and asymmetrical attractors.     

The capacity of two neighbour intersections considering the influence of the bus stop

In this paper, we use a two-lane CA model to investigate the effect of a bus stop between two neighbouring intersections on the capacity of the bus. Both the case of a bus stop with a special stopping lane and that of one without are considered. The capacity versus the distance L_B(L_D) between the stop and the upstream (downstream) intersection is studied, with respect to the entering probability P_e and the traffic light cycle T. It is found that a bus stop near an intersection can act as a bottleneck and cause a drop in the capacity when the L_B (or L_D) is below a critical point L_Bc1(or L_Dc1). However, the situation when the stop is located near the downstream intersection is worse than that of the upstream one. Furthermore, the simulation results show that the negative effect varies with the increase of the cycle time T and the capacity can be maximized by adjusting T. Comparisons between the two cases suggest that the stopping lane can improve the capacity to some extent. These results mean that the capacity can be exploited by changing the position of the bus stop or the cycle time, and adding a stopping lane if necessary. These findings may be useful in offering scientific guidance for the management and design of traffic networks.     

Absence of hyperscaling violations for phase transitions with positive specific heat exponent

Finite size scaling theory and hyperscaling are analyzed in the ensemble limit which differs from the finite size scaling limit. Different scaling limits are discussed. Hyperscaling relations are related to the identification of thermodynamics as the infinite volume limit of statistical mechanics. This identification combined with finite ensemble scaling leads to the conclusion that hyperscaling relations cannot be violated for phase transitions with strictly positive specific heat exponent. The ensemble limit allows to derive analytical expressions for the universal part of the finite size scaling functions at the critical point. The analytical expressions are given in terms of generalH-functions, scaling dimensions and a new universal shape parameter. The universal shape parameter is found to characterize the type of boundary conditions, symmetry and other universal influences on critical behaviour. The critical finite size scaling functions for the order parameter distribution are evaluated numerically for the cases =3, =5 and =15 where is the equation of state exponent. Using a tentative assignment of periodic boundary conditions to the universal shape parameter yields good agreement between the analytical prediction and Monte-Carlo simulations for the two dimensional Ising model. Analytical expressions for critical amplitude ratios are derived in terms of critical exponents and the universal shape parameters. The paper offers an explanation for the numerical discrepancies and the pathological behaviour of the renormalized coupling constant in mean field theory. Low order moment ratios of difference variables are proposed and calculated which are independent of boundary conditions, and allow to extract estimates for a critical exponent.     

Towards a dynamical temperature of finite Hamiltonian systems

With the aid of numerical simulations of the β Fermi-Pasta-Ulam (FPU) system, we compare the different definitions of dynamical temperature for Hamiltonian systems. We have shown that each definition gives different values of temperature for a system with a small number of degrees of freedom (DOF). Only for systems with a sufficiently large number of DOF, do all the definitions of dynamical temperature approach the same value.     

Mode-Locking Behaviour in Driven Colloids with Random Pinning

We find mode-locking steps in simulated force-velocity characteristics of external alternating-force （AF） driven colloids on a disordered substrate. Studies of mode-locking patterns in systems show that mode-locking steps are accompanied with the emergence of a dynamics phase： transverse solid phase. We also study the influence of temperature on the width of mode-locking steps. The mode-locked state is destroyed by thermal fluctuation and the width of mode-locking steps decreases rapidly with increasing temperature. In high velocity and low temperature regimes, due to the appearance of transverse solid phase and microscopically periodic velocity modulation, the step width changes little as temperature is varied.     

Multiple-mode wave solutions in Vakhnenko equation

A new type of wave solutions, called as multiple-mode waves, which can be expressed in the superposition forms of more than two types of single-mode waves of Vakhnenko equation have been investigated in this Letter. A new general method for obtaining the multiple-mode waves is proposed, based on which four cases of the possible forms of wave solutions with two-mode have been derived. The explicit expressions of the two-mode waves as well as the existence conditions have been presented, which may be the nonlinear combinations between periodic waves, solitons, compactons, etc., with different wave speeds, respectively. It is pointed out that more complicated multiple-mode waves with more than three single-mode waves can be derived accordingly, which can be used to reveal the evolution of interactions between different types of waves, especially between various solitons.     

A new macro model with consideration of the traffic interruption probability

In this paper, we present a new macro model which involves the effects that the probability of traffic interruption has on the car-following behavior through formulating the inner relationship between micro and macro variables. Linear stability analysis shows that consideration of the traffic interruption probability can improve the stability of traffic flow if and only if the drivers’ reactive time required for adjusting their acceleration based on the traffic interruption probability p is not greater than that one based on the non-interruption probability 1−p. Numerical results verify that the new model can be used to analyze the effects of traffic interruption probability and traffic interruption on shock, rarefaction wave, small perturbation and uniform flow. The model has been applied in reproducing some complex traffic phenomena resulted by some traffic interruptions (e.g., signal light, pedestrian and tolling station).     

Logarithmic frequency scaling of semiconductor oscillations caused by a modified saddle-node bifurcation on a limit cycle

The oscillatory behavior of low-temperature impact ionization breakdown inp-type germanium is investigated experimentally. We explain the anomalous scaling behavior of a saddle-node bifurcation on a limit cycle in terms of a simple model approach. It represents the low-dimensional analog to a new type of intermittency proposed recently.     

Competition of Multi-Agent Systems: Analysis of a Three-Company Econophysics Model

A three-company econophysics model for competing multi-agent systems in a triangular lattice is analyzed using mean field theory for its phase diagram. Interpretations for the temperature, spin density and lattice structures are presented. Suggestions for the use of this model for econophysics in the context of multi-agent systems are made.     

Subconscious Effect on Pedestrian Counter Flow

We propose an extended lattice gas model with different maximum velocities to simulate pedestrian counter flow by considering the subconscious behaviour of walkers. Four types of walkers including faster right walkers, slower right walkers, faster left walkers and slower left walkers are involved in the simulation. The simulation results show that our model can capture some essential features of pedestrian counter flows, such as the lane formation, segregation effect and phase separation at higher densities. We also find that the subconscious effect can reduce the occurrence of jam cluster evidently compared with the ease of un-subeonscious effect. At large maximum velocity, the critical density corresponding to the maximum flow rate of the fundamental diagram is in good agreement with the empirical results.     

Delay-enhanced coherence of spiral waves in noisy Hodgkin-Huxley neuronal networks

We study the spatial dynamics of spiral waves in noisy Hodgkin-Huxley neuronal ensembles evoked by different information transmission delays and network topologies. In classical settings of coherence resonance the intensity of noise is fine-tuned so as to optimize the system's response. Here, we keep the noise intensity constant, and instead, vary the length of information transmission delay amongst coupled neurons. We show that there exists an intermediate transmission delay by which the spiral waves are optimally ordered, hence indicating the existence of delay-enhanced coherence of spatial dynamics in the examined system. Additionally, we examine the robustness of this phenomenon as the diffusive interaction topology changes towards the small-world type, and discover that shortcut links amongst distant neurons hinder the emergence of coherent spiral waves irrespective of transmission delay length. Presented results thus provide insights that could facilitate the understanding of information transmission delay on realistic neuronal networks.     

Stabilizability of discrete chaotic systems via unified impulsive control

This Letter is concerned with the asymptotical stabilization problem of discrete chaotic systems by using a novel unified impulsive control scheme. Sufficient conditions for asymptotical stability of the impulsive controlled discrete systems are obtained by means of the Lyapunov stability theory and algebraic inequality techniques. Finally, numerical simulations on the Hénon and Ushio discrete chaotic systems are presented to illustrate the effectiveness and usefulness of the unified impulsive control scheme.     

Characterizing dynamical transitions in bistable systems using a non-equilibrium measurement of work

We show how the Jarzynski relation can be exploited to analyze the nature of order-disorder, and a bifurcation type dynamical transition in terms of a response function derived on the basis of work distribution over non-equilibrium paths between two thermalized states. The validity of the response function extends over a linear as well as a nonlinear regime, and far from equilibrium situations.     

Analysis of heartbeat asymmetry based on multi-scale time irreversibility test

We investigate the asymmetry of heart rate control system and suggest a simple index to quantify this asymmetry by performing high-dimensional time irreversibility tests to heartbeat interval time series over multiple scales. The results provide strong evidence to the concept that the asymmetry is an intrinsic property of heart rate control system. As a simple and visual method, it is proved to be effective in classifying physiologic and synthetic subjects while the maximum scale is selected within a proper range, and also provides a new way to analyze the time irreversibility for other high-dimensional systems.     

New universal bifurcation scenario in one-dimensional trimodal maps

By means of star products and high precision numerical calculation, an abnormal phenomenon is found in period-p-tupling bifurcation processes in one-dimensional trimodal maps. A route of transition to chaos, presented by a right-associative non-normal star product, breaks the Feigenbaum's metric universality, namely, the conventional Feigenbaum's successive rates exhibit a strong divergence. To overcome the divergence, an approximate scheme of accelerating convergence is proposed; and the Feigenbaum scenario is included as a special case in the new bifurcation scenario. It will provide access to understanding non-normal star products and their corresponding renormalization.