Nonlinear Dynamic Stability of Normal and Arthritic Greyhounds

In this paper the dynamic stability of greyhound gait was analyzed within the framework of nonlinear dynamics theory. A video based motion analysis system was utilized to obtain the kinematic data of the hindlimb joints of greyhounds at trot. Phase plane portraits and first return maps for the coxofemoral, femorotibial, and the tarsal joints were calculated from averaged kinematic data for each dog. The analysis was based on the assumption that the steady state dog locomotion could be represented as a nonlinear periodic system. Using the Floquet theory, the dynamic stability of gait was quantified by computing the characteristic multipliers from experimental data. A stability index based on multipliers was used for comparison between normal and arthritic dogs. Phase plane portraits and first return maps of the dogs with transient synovitis were compared with the averaged portraits of the normal dogs. It was observed that the coxofemoral angle exhibited the maximum difference while the femorotibial and the tarsal joints showed little or no difference from those of the normals. Comparison of the Floquet multipliers indicated that the dogs with synovitis had a less stable gait than that of the normal dogs.     

Bifurcation and Chaos in an Apparent-Type Gyrostat Satellite

Attitude dynamics of an asymmetrical apparent gyrostat satellite has been considered. Hamiltonian approach and Routhian are used to prove that the dynamics of the system consists of two separate parts, an integrable and a non-integrable. The integrable part shows torque free motion of gyrostat, while the non-integrable part shows the effect of rotation about the earth and asphericity of the satellites inertia ellipsoid. Using these results, theoretically when the non-integrable part is eliminated, we are able to design a satellite with exactly regular motion. But from the engineering point of view the remaining errors of manufacturing process of the mechanical parts cause that the non-integrable part can not be eliminated, completely. So this case can not be achieved practically. Using Serret–Andoyer canonical variable the Hamiltonian transformed to a more appropriate form. In this new form the effect of the gravity, asphericity, rotational motion and spin of the rotor are explicitly distinguished. The results lead us to another way of control of chaos. To suppress the chaotic zones in the phase space, higher rotational kinetic energy can be used. Increasing the parameter related to the spin of the rotor causes the systems phase space to pass through a heteroclinic bifurcation process and for the sufficiently large magnitude of the parameter the heteroclinic structure can be eliminated. Local bifurcation of the phase space of the integrable part and global heteroclinic bifurcation of whole systems phase space are presented. The results are examined by the second order Poincaré surface of section method as a qualitative, and the Lyapunov characteristic exponents as a quantitative criterion.     

神经网络时滞系统非共振双Hopf分岔及其广义同步

本文建立了具有自连接和抑制-兴奋型他连接的两个同性神经元模型。其中自连接是由于兴奋型的突触产生,而他连接则分别对应于两神经元兴奋、抑制型的突触。发现如果有兴奋型自连接就会有双Hopf分岔,而没有时滞自连接时双Hopf分岔就会消失,因此自连接引起了双Hopf分岔。作为一个例子,通过变动连接中的时滞和他连接中的比重,1／√2双Hopf分岔得到了详细研究。通过中心流形约化,分岔点邻域内各种不同的动力学行为得到了分类,并以解析形式表出。神经元活动的分岔路径得以表明。从得到的解析近似解可以发现,本文所研究的具有兴奋一抑制型他连接的两相同神经元的节律不能完全同步而只能广义同步。时滞也可以使其节律消失,两神经元变为非活动的。这些结果在控制神经网络关联记忆和设计人工神经网络方面有着潜在的应用。     

模糊—神经网络控制算法及其在离心力—振动复合环境试验系统中的应用

针对离心－振动复合环境试验系统所存在的耦合性、非线性和不确定性提出了一种模糊－神经网络控制算法,利用被控对象输入输出信息离线、在线相结合学习系统的动态特性,对时变、非线性系统进行跟踪控制,并研究了该算法在系统中的实现方法。实现表明了控制系统具有良好的跟踪能力。该算法也适用于快速变化这类系统的实时控制。