An extended two-lane traffic flow lattice model with driver’s delay time

In this paper, a new two-lane lattice model is presented by considering the effect of drivers’ delay in sensing relative flux. By means of the linear stability analysis, the effect of drivers’ delay time on the stability of two-lane traffic flow is examined and shown that with the drivers’ delay time increasing, the unstable areas expand accordingly on the phase diagram, which is also confirmed by direct computer simulations. Through nonlinear analysis method, the modified Korteweg–deVries equation near the critical point is obtained and solved to describe the traffic- jamming transitions in a two-lane system.     

Lattice hydrodynamic traffic flow model with explicit drivers’ physical delay

An extended lattice hydrodynamic model is presented by considering the effect of drivers’ delay in sensing relative flux. The linear stability criterion of the new model is obtained by employing the linear stability theory. By means of nonlinear analysis method, the modified Korteweg–deVries (mKdV) equation near the critical point is constructed and solved. The propagation behavior of traffic jam can thus be described by the kink–antikink soliton solution for the mKdV equation. The good agreement between the simulation results and the analytical results show that the drivers’ delay in sensing relative flux effect plays an important role in traffic jamming transition.     

Optimal control of phytoplankton–fish model with the impulsive feedback control

Nonlinear Dynamics - Considering how to exploit the lake resource reasonably, we propose a phytoplankton–fish model with the impulsive feedback control and investigate the sufficient...     

Analyses of the driver’s anticipation effect in a new lattice hydrodynamic traffic flow model with passing

In this paper, we studied the effect of driver’s anticipation with passing in a new lattice model. The effect of driver’s anticipation is examined through linear stability analysis and shown that the anticipation term can significantly enlarge the stability region on the phase diagram. Using nonlinear stability analysis, we obtained the range of passing constant for which kink soliton solution of mKdV equation exist. For smaller values of passing constant, uniform flow and kink jam phase are present on the phase diagram and jamming transition occurs between them. When passing constant is greater than the critical value depending on the anticipation coefficient, jamming transitions occur from uniform traffic flow to kink-bando traffic wave through chaotic phase with decreasing sensitivity. The theoretical findings are verified using numerical simulation which confirm that traffic jam can be suppressed efficiently by considering the anticipation effect in the new lattice model.     

Hopf bifurcation for a small-world network model with?parameters delay feedback control

To delay the onset of undesirable bifurcation, the bifurcation control has become a subject of intense research activities. In this paper, a small-world network model with the delay feedback is considered, in which the strength of feedback control is a nonlinear function of delay. With this controller, one can change the critical value of bifurcation, and thus enlarge the stable region. Moreover, by adding some proper slowly varying parts into the bifurcation parameters, the stability can be improved. Numerical results show that the dynamics of the small-world network model with the controller of delay-dependent parameters is quite different from that of a system with the controller of delay-independent parameters only.     

The self-stabilization effect of lattice’s historical flow in a new lattice hydrodynamic model

In order to reveal the self-stabilization effect of the lattice’s historical information on traffic flow, a new lattice hydrodynamic model with consideration of the considered lattice’s historical flow is proposed. The impact of the lattice’s historical flow on traffic stability is uncovered through theoretical analyses and numerical simulation. Through theoretical analyses, the linear stability condition of the new model is obtained, and the nonlinear mKdV equation is derived to describe traffic jamming transition of the new model near the critical point. From numerical simulation, the theoretical analyses are verified and it is shown that the traffic stability can be enhanced by considering the current lattice’s self-information of its historical flow.     

Impact of lattice’s self-anticipative density on traffic stability of lattice model on two lanes

Nonlinear Dynamics - The self-anticipative density (SAD) term is embedded to traffic modeling for two-lane freeway in this paper. In view of linear stability analysis, SAD effect on two lanes is...     

TDGL equation in lattice hydrodynamic model considering driver’s physical delay

Based on an extended lattice hydrodynamic model considering the delay of the driver’s response in sensing headway, we get the time-dependent Ginzburg–Landau (for short, TDGL) equation to describe the transition and critical phenomenon in traffic flow by applying the reductive perturbation method. The corresponding solutions are obtained. Numerical simulation is carried out to examine the performance of the model and the results show coincidence with the analysis results.     

Pointwise-in-space stabilization and synchronization of a class of reaction–diffusion systems with mixed time delays via aperiodically impulsive control

Nonlinear Dynamics - This paper investigates the problems of pointwise-in-space stabilization and synchronization of semilinear reaction–diffusion systems with Dirichlet boundary conditions...     

Integral-based event-triggered synchronization criteria for chaotic Lur’e systems with networked PD control

Integral-based event-triggered synchronization criteria are firstly presented for networked chaotic systems with proportional-derivative (PD) control. The event-triggered scheme effectively utilizes network resources; however, the PD-type control subject to the conventional triggering inequality may cause excessive triggering and have difficulty in obtaining a feasible solution. To solve these problems, the integrated event-triggering inequality is employed and the modified integral inequality with free-weighting matrix is proposed to fill the empty diagonal terms, which overcomes the difficulties of the integration of delayed signal vectors upon integral event-triggering condition. Based on Lyapunov stability, the synchronization criteria are derived as linear matrix inequalities. Finally, the effectiveness of the integral-based event-triggered synchronization method is demonstrated by numerical examples.     

A feedback linearization design for the control of vehicle’s lateral dynamics

In this paper, the feedback linearization scheme is applied to the control of vehicle’s lateral dynamics. Based on the assumption of constant driving speed, a second-order nonlinear lateral dynamical model is adopted for controller design. It was observed in (Liaw, D.C., Chung, W.-C. in 2006 IEEE International Conference on Systems, Man, and Cybernetics, 2006) that the saddle-node bifurcation would appear in vehicle dynamics with respect to the variation of the front wheel steering angle, which might result in spin and/or system instability. The vehicle dynamics at the saddle node bifurcation point is derived and then decomposed as an affine nominal model plus the remaining term of the overall system dynamics. Feedback linearization scheme is employed to construct the stabilizing control laws for the nominal model. The stability of the overall vehicle dynamics at the saddle-node bifurcation is then guaranteed by applying Lyapunov stability criteria. Since the remaining term of the vehicle dynamics contains the steering control input, which might change system equilibrium except the designed one. Parametric analysis of system equilibrium for an example vehicle model is also obtained to classify the regime of control gains for potential behavior of vehicle’s dynamical behavior.     

Wave features of a hyperbolic reaction–diffusion model for Chemotaxis

The Extended Thermodynamic theory is used to derive a hyperbolic reaction–diffusion model for Chemotaxis. Linear stability analysis is performed to study the nature of the equilibrium states against uniform and nonuniform perturbations. A particular emphasis is given to the occurrence of the Turing bifurcation. The existence of traveling wave solutions connecting the two steady states is investigated and the governing equations are numerically integrated to validate the analytical results. The propagation of plane harmonic waves is analyzed and the stability regions in terms of the model parameters are shown. The frequency dependence of the phase velocity and of the attenuation is also illustrated. Finally, in order to have a measure of the non linear stability, the propagation of acceleration waves is studied, the wave amplitude is derived and the critical time is evaluated.     

Stokes＇ first problem for a viscoelastic fluid with the generalized Oldroyd-B model

The flow near a wall suddenly set in motion for a viscoelastic fluid with the generalized Oldroyd-B model is studied. The fractional calculus approach is used in the constitutive relationship of fluid model. Exact analytical solutions of velocity and stress are obtained by using the discrete Laplace transform of the sequential fractional derivative and the Fox H-function. The obtained results indicate that some well known solutions for the Newtonian fluid, the generalized second grade fluid as well as the ordinary Oldroyd-B fluid, as limiting cases, are included in our solutions. The project supported by the National Natural Science Foundation of China (10272067), the Doctoral Program Foundation of the Education Ministry of China (20030422046), the Natural Science Foundation of Shandong Province, China (Y2006A14) and the Research Foundation of Shandong University at Weihai. The English text was polished by Keren Wang.     

Observer-based dissipative output feedback control for network T–S fuzzy systems under time delays with mismatch premise

Nonlinear Dynamics - This paper deals with the problem of non-parallel distribution compensation networked control systems (NCSs) under event-triggered strategy based on the fuzzy system for a...     

Stabilizing control of Hopf bifurcation in the Hodgkin–Huxley model via washout filter with linear control term

It is a significant issue to control bifurcation because many neuronal diseases have close relevance to bifurcation of neuron system. Some studies have been done on bifurcation control in the Hodgkin–Huxley (HH) model, but there is no clear mathematical criterion for bifurcation stabilization. In this paper, according to Routh–Hurwitz stability criterion, we employ linear control term of washout filter-aided dynamic feedback controller to stabilize bifurcation of the HH model. As a result, we can deduce linear control gain based on the criterion, and simulation shows the method is effective for making the HH model stable. The controller designs described here are achieved by electrical stimulus, so it may have potential applications in the diagnosis and therapy of dynamical diseases.