In this paper,a new nonlinear autonomous system introduced by Chlouverakis and Sprott is studied further,to present very rich and complex nonlinear dynamical behaviors. Some basic dynamical properties are studied eith...In this paper,a new nonlinear autonomous system introduced by Chlouverakis and Sprott is studied further,to present very rich and complex nonlinear dynamical behaviors. Some basic dynamical properties are studied either analytically or nu-merically,such as Poincaré map,Lyapunov exponents and Lyapunov dimension. Based on this flow,a new almost-Hamilton chaotic system with very high Lyapunov dimensions is constructed and investigated. Two new nonlinear autonomous systems can be changed into one another by adding or omitting some constant coefficients.展开更多
Traditional biomechanical analyses of human movement are generally derived from linear mathematics.While these methods can be useful in many situations,they do not describe behaviors in human systems that are predomin...Traditional biomechanical analyses of human movement are generally derived from linear mathematics.While these methods can be useful in many situations,they do not describe behaviors in human systems that are predominately nonlinear.For this reason,nonlinear analysis methods based on a dynamical systems approach have become more prevalent in recent literature.These analysis techniques have provided new insights into how systems(1) maintain pattern stability,(2) transition into new states,and(3) are governed by short-and long-term(fractal) correlational processes at different spatio-temporal scales.These different aspects of system dynamics are typically investigated using concepts related to variability,stability,complexity,and adaptability.The purpose of this paper is to compare and contrast these different concepts and demonstrate that,although related,these terms represent fundamentally different aspects of system dynamics.In particular,we argue that variability should not uniformly be equated with stability or complexity of movement.In addition,current dynamic stability measures based on nonlinear analysis methods(such as the finite maximal Lyapunov exponent) can reveal local instabilities in movement dynamics,but the degree to which these local instabilities relate to global postural and gait stability and the ability to resist external perturbations remains to be explored.Finally,systematic studies are needed to relate observed reductions in complexity with aging and disease to the adaptive capabilities of the movement system and how complexity changes as a function of different task constraints.展开更多
The constitutive behavior of microcrystals remains mysterious since very little,or no information regarding plastic deformation in the measured stress-strain curve is available due to plastic instability.Furthermore,t...The constitutive behavior of microcrystals remains mysterious since very little,or no information regarding plastic deformation in the measured stress-strain curve is available due to plastic instability.Furthermore,the measured stress-strain curves vary greatly under different control modes,while constitutive behavior should remain unaffected by test methods.Beyond these reasons,probing the real constitutive behavior of microcrystals has long been a challenge because the nonlinear dynamical behaviors of micromechanical testing systems are unclear.Here,we perform and carefully analyze the experiments on singlecrystal aluminum micropillars under displacement control and load control.To interpret these experimental results,a lumpedparameter physical model based on the principle of micromechanical testing is developed,which can directly relate nonlinear dynamics of the micromechanical testing system to the constitutive behavior of microcrystals.This reveals that some stages of the measured stress-strain curve attributed to the control algorithm are not related to constitutive behavior.By solving the nonlinear dynamics of the micromechanical testing system,intense plastic instability(large strain burst)starting from the equilibrium state is attributed to the strain-softening stage of microcrystals.Parametric studies are also performed to reduce the influence of plastic instability on the measured responses.This study provides critical insights for developing various constitutive models and designing a reliable micromechanical testing system.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 50475109)the Natural Science Foundation of Gansu Province (No. 3ZS-042-B25-049), China
文摘In this paper,a new nonlinear autonomous system introduced by Chlouverakis and Sprott is studied further,to present very rich and complex nonlinear dynamical behaviors. Some basic dynamical properties are studied either analytically or nu-merically,such as Poincaré map,Lyapunov exponents and Lyapunov dimension. Based on this flow,a new almost-Hamilton chaotic system with very high Lyapunov dimensions is constructed and investigated. Two new nonlinear autonomous systems can be changed into one another by adding or omitting some constant coefficients.
文摘Traditional biomechanical analyses of human movement are generally derived from linear mathematics.While these methods can be useful in many situations,they do not describe behaviors in human systems that are predominately nonlinear.For this reason,nonlinear analysis methods based on a dynamical systems approach have become more prevalent in recent literature.These analysis techniques have provided new insights into how systems(1) maintain pattern stability,(2) transition into new states,and(3) are governed by short-and long-term(fractal) correlational processes at different spatio-temporal scales.These different aspects of system dynamics are typically investigated using concepts related to variability,stability,complexity,and adaptability.The purpose of this paper is to compare and contrast these different concepts and demonstrate that,although related,these terms represent fundamentally different aspects of system dynamics.In particular,we argue that variability should not uniformly be equated with stability or complexity of movement.In addition,current dynamic stability measures based on nonlinear analysis methods(such as the finite maximal Lyapunov exponent) can reveal local instabilities in movement dynamics,but the degree to which these local instabilities relate to global postural and gait stability and the ability to resist external perturbations remains to be explored.Finally,systematic studies are needed to relate observed reductions in complexity with aging and disease to the adaptive capabilities of the movement system and how complexity changes as a function of different task constraints.
基金supported by the National Natural Science Foundation of China(Grant Nos.51731009,12102216,and 11972205)the Fundamental Research Funds for the Central Universities(Grant No.2020XZZX005-02)the China Postdoctoral Science Foundation(Grant Nos.2021M691796,and 2021T140379).
文摘The constitutive behavior of microcrystals remains mysterious since very little,or no information regarding plastic deformation in the measured stress-strain curve is available due to plastic instability.Furthermore,the measured stress-strain curves vary greatly under different control modes,while constitutive behavior should remain unaffected by test methods.Beyond these reasons,probing the real constitutive behavior of microcrystals has long been a challenge because the nonlinear dynamical behaviors of micromechanical testing systems are unclear.Here,we perform and carefully analyze the experiments on singlecrystal aluminum micropillars under displacement control and load control.To interpret these experimental results,a lumpedparameter physical model based on the principle of micromechanical testing is developed,which can directly relate nonlinear dynamics of the micromechanical testing system to the constitutive behavior of microcrystals.This reveals that some stages of the measured stress-strain curve attributed to the control algorithm are not related to constitutive behavior.By solving the nonlinear dynamics of the micromechanical testing system,intense plastic instability(large strain burst)starting from the equilibrium state is attributed to the strain-softening stage of microcrystals.Parametric studies are also performed to reduce the influence of plastic instability on the measured responses.This study provides critical insights for developing various constitutive models and designing a reliable micromechanical testing system.
