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The modelling theory of the optimal low-dimensional dynamical system of the fluctuation velocity equations of the Navier-Stokes equations was studied. The optimal target functional is the incompressibility and orthogonality of the fluctuation velocity basis function. The fully developed side-by-side two-column flow problem was numerically simulated. Based on the two-scale global optimization method, the optimal dynamical system model for its fluctuation velocity was established. The dynamics properties of the phase portraits, the Poincaré section, the bifurcation characteristics, the power spectrum and the Lyapunov exponent set were analyzed. With the increase of the Reynolds number, the optimal dynamical systems of the fluctuation velocity equations of the flow around the two columns exhibit complex quasi-periodic bifurcation behaviors. [ABSTRACT FROM AUTHOR]

The modeling method for the optimal dynamical systems of Navier-Stokes equations satisfying both arbitrary velocity boundary conditions and velocity incompressible conditions was studied. Through the modeling and analysis of the optimal dynamical systems of the flow around the square column, it is found that the dynamics characteristics of the optimal dynamical systems are limit cycles. At the same time, the optimal dynamical system with only 3 optimal basis functions could well describe all the main flow field characteristics and the dynamics characteristics of the problem, so the proposed method is applicable to complex flow problems and their dynamics with minimal basis functions. [ABSTRACT FROM AUTHOR]

Can the extended mind explain the intentional behavior? Cleland argues that the extended mind theory forces us to give up our causal sovereignty when it comes to our actions, and therefore renders us not agentially responsible for them. If the extended mind theory is metaphysically incompatible with this very idea, the theory includes a deep inconsistency. The main reason for this is that the explanation on behavior by extended mind would not conform to Davidson's argument of "motivation-causality". However, Davidson's argument has its own drawbacks. It does not explain how meaning flows into behavior. A better approach is to reinterpret "the agential control" with the top-down causality. [ABSTRACT FROM AUTHOR]

With the dynamical system method, the qualitative performance of and the exact travelling wave solutions to the coupled Higgs equations and the Maccari systems were studied. Based on this method, all phase portraits of the systems in the parametric space were given. All possible bounded travelling wave solutions such as the solitary wave solutions and the periodic travelling wave solutions were obtained. Through numerical simulation, the smooth solitary wave solutions and the periodic travelling wave solutions were picturized. The results show that the present findings improve the related previous conclusions. [ABSTRACT FROM AUTHOR]

We propose a dynamical system model to formulate day-to-day traffic assignment. This model describes the dynamic adjustment process of route flows from day to day and its stationary state is equivalent to the Logit stochastic user equilibrium state. We also analyze several properties of the model, including the equivalence between the stationary state and user equilibrium state and the uniqueness and convergence of its stationary point. The model is given in discrete and general form and hence we introduce a special case of the model. Finally, we apply the model to a numerical example to illustrate its application and properties. The study is helpful for better understanding the adjustment process of route flows from day to day. [ABSTRACT FROM AUTHOR]

A dynamical system concerning intracellular substances and transport patterns was proposed to describe glycerol bioconversion to 1, 3-propanediol in continuous fermentation process. Some properties of the system were subsequently discussed. Taking the error between the computational values and experimental data as the cost function, a parameter identification model to identify the intracellular kinetic parameters was established. The existence of the optimal parameters in the parameter identification model was also proved. Finally, an improved particle swarm optimization was constructed to solve the above parameter identification model. Numerical results show that the mean relative error is cut down by 20. 635 %, and the proposed algorithm has higher global convergence compared with other optimization algorithms. [ABSTRACT FROM AUTHOR]

Prediction of trends for time series is investigated by the dynamical systems methods. Several methods of extracting the trends of time series are compared by the aid of the error measurement model derived from Copula functions. The constructing method of the comparison criterion is innovated. Using the trends of time series data,the prediction of the stock market index through the dynamical system demonstrates the validity of this method. [ABSTRACT FROM AUTHOR]

A numerical gradient algorithm was proposed to solve a constrained optimization problem arising from a nearestness problem in SO(n), which can be viewed as a discrete dynamical system algorithm. The main advantage of the method is that the iterative sequence always satisfies the constrained condition. The convergence analysis and asymptotical stability analysis were established, and the numerical experiments show the effectiveness and reliability of the algorithm. [ABSTRACT FROM AUTHOR]