Stability and boundary equilibrium bifurcations of modified Chua's circuit with smooth degree of 3

Chua＇s circuit is a well-known nonlinear electronic model, having complicated nonsmooth dynamic behaviors. The stability and boundary equilibrium bifurcations for a modified Chua＇s circuit system with the smooth degree of 3 are studied. The parametric areas of stability are specified in detail. It is found that the bifurcation graphs of the su- percritical and irregular pitchfork bifurcations are similar to those of the piecewise-smooth continuous （PWSC） systems caused by piecewise smoothness. However, the bifurcation graph of the supercritical Hopf bifurcation is similar to those of smooth systems. There- fore, the boundary equilibrium bifurcations of the non-smooth systems with the smooth degree of 3 should receive more attention due to their special features.

GROUNDWATER MASS TRANSPORT AND HOMOGENEOUS EQUILIBRIUM CHEMISTRY IN THE PRESENCE OF FLUX BOUNDARY CONDITIONS

Considering a solute transport problem deseribed by some algebraic and partial differentialequations with the presence of flux boundary conditions, we reduce the problem to a fixed point oneand use a priori estimates to prove the existence and uniqueness of the global solutions.

Complex Dynamical Behaviors in a Dual Channel Supply Chain Model with Retailer's Service Input

Based on bounded rationality,this paper established a price game model of dual channel supply chain composed of manufacturers and retailers.According to the eigenvalue of Jacobi matrix and Jury criterion,the stability of the equilibrium point is analyzed,and then the dynamic evolution process under the parameters of price adjustment speed and retailer's service input is studied through stability region,bifurcation diagram,maximum Lyapunov exponent diagram and attraction basin.The results show that the system enters chaos through flip and Neimark-Sacker bifurcation,and increase of price adjustment speed and service input value will make the system produce more dynamic behavior.In addition,it can be found that the impact of service input value on itself is much greater than that on manufacturers.Secondly,when adjustment speed is selected as bifurcation parameter,the change curve of sales price is inconsistent,in which the change of retailers mainly remains in periodic state,while manufacturers will gradually enter chaos.Finally,studies the evolution of attraction basin in which three kinds of attractors coexist.In particular,coexistence of boundary attractors and internal attractors increases the complexity of system.Therefore,enterprises need to carefully adjust parameters of the game model to control the stability of system and maintain the long-term stability of market competition.

Some important aspects of wind-resistant studies on long-span bridges

In recent years many long-span bridges have been or are being constructed in the world, especially in China. Wind loads and responses are the key factors for their structural design. This paper introduces some important achievements of wind-resistant studies of the author's research team on long-span bridges. First, new concepts and identification methods of aerodynamic derivatives and aerodynamic admittances were proposed. Then mechanical and aerodynamic control strategies and methods of wind-induced vibrations of long-span bridges were the great concerned problems, and valuable achievements were presented. Especially, great efforts which have been theoretically and experimentally made on rain-wind induced vibration of cables of cable-stayed bridges were described. Finally, some new progresses in computation wind engineering were introduced, and a new method for simulating an equilibrium boundary layer was put forward as well.