Several Neutral Dynamical Systems And Its Application In Forestry Engineering

Neutral dynamical systems are often used for describing evolutionary systems, in which current growth rate depends on that in the past. Such systems are widely applied to lossless transmission line, ecosystem and control theory. The research on the stability and Hopf bifurcation helps revealing the complicated dynamical behavior in these systems. In this paper, two kinds of neutral neural network systems are studied in following aspects:stability, oscillation, Hopf bifurcation properties and global Hopf bifurcation. As to the applications of neutral dynamical systems, the use of neutral dynamical systems in forestry engineering is investigated, which includes fruit picking through mechanical vibration and fault signal detection and torsional vibration control of woodworking rotating machinery.First of all, the dynamics properties of a kind of 2-dimensional neutral neural network are investigated. With different theories, research on four issues are carried on:(1) the stability, Pitchfork bifurcation and the existence of Hopf bifurcation of the network are investigated by using the stability theory; (2) the properties of Hopf bifurcation (including the direction of bifurcation and stability of bifurcating periodic solutions) are investigated by using the center manifold theory and normal form method; (3) the global Hopf bifurcation is investigated through the global Hopf theorem and higher dimensional Bendixon criterion; (4) the existence of vibration solutions are investigated by using Chafee limit cycle theorem. Moreover, the dynamics properties of another kind of simplified neutral BAM neural network model are investigated. The stable region of the model is given within the parameter plane. The existence conditions of global Hopf bifurcation of the model are investigated through the second order complex matrix theory.Secondly, the application of neutral dynamical systems in fruit picking theory by using mechanical vibration is studied. By introducing factors like nonlinear equivalent elastic stiffness and time-delay damping, the existing harvesting machine-fruit tree linear vibration model is modified into a delayed and neutral type nonlinear model. The stability of fruit tree vibration system without external excitation is investigated through dynamical system stability theory. With the average method, the nonautonomous vibration system with external excitation is converted to an approximate autonomous system. And in the way, the work of periodic solutions for a nonautonomous system is transformed into the research of equilibrium point for an autonomous system. The conditions of periodic vibration existence and stability in the fruit trees vibration model are obtained. This method overcomes the difficulty that the system has no small parameter.Finally, the application of neutral dynamical systems in both fault signal detection and torsional vibration control of woodworking rotating machinery is studied. On one side, three feed-forward coupled van del Pol oscillators model with delay is constructed and the dynamics properties including stability and bifurcation are analyzed. In addition, the methods and effects of the using of neutral dynamical systems in the case of the amplitude enhancement of weak signal are investigated through the nonlinear growth principle of Hopf bifurcation. On the other side, a new method of vibration suppression of torsional vibrating system is established by using the delayed vibration absorber of neutral type. The stability theory of dynamical systems is applied to analyze the stability of the neutral delayed vibration absorber and the torsional vibrating system and the stability switch method is applied to obtain the damping effect. It can be concluded that the neutral delayed vibration absorber has a better damping effectthan any other delayed and tradition vibration absorber and is suitable for practical use.