Studies of phase return map and symbolic dynamics in a periodically driven Hodgkin–Huxley neuron

How neuronal spike trains encode external information is a hot topic in neurodynamics studies. In this paper, we investigate the dynamical states of the Hodgkin-Huxley neuron under periodic forcing. Depending on the parameters of the stimulus, the neuron exhibits periodic, quasiperiodic and chaotic spike trains. In order to analyze these spike trains quantitatively, we use the phase return map to describe the dynamical behavior on a one-dimensional （1D） map. According to the monotonicity or discontinuous point of the 1D map, the spike trains are transformed into symbolic sequences by implementing a coarse-grained algorithm -- symbolic dynamics. Based on the ordering rules of symbolic dynamics, the parameters of the external stimulus can be measured in high resolution with finite length symbolic sequences. A reasonable explanation for why the nervous system can discriminate or cognize the small change of the external signals in a short time is also presented.

Analysis on the Performance of the SLIP Runner with Nonlinear Spring Leg

The spring-loaded inverted pendulum(SLIP) has been widely studied in both animals and robots.Generally,the majority of the relevant theoretical studies deal with elastic leg,the linear leg length-force relationship of which is obviously conflict with the biological observations.A planar spring-mass model with a nonlinear spring leg is presented to explore the intrinsic mechanism of legged locomotion with elastic component.The leg model is formulated via decoupling the stiffness coefficient and exponent of the leg compression in order that the unified stiffness can be scaled as convex,concave as well as linear profile.The apex return map of the SLIP runner is established to investigate dynamical behavior of the fixed point.The basin of attraction and Floquet Multiplier are introduced to evaluate the self-stability and initial state sensitivity of the SLIP model with different stiffness profiles.The numerical results show that larger stiffness exponent can increase top speed of stable running and also can enlarge the size of attraction domain of the fixed point.In addition,the parameter variation is conducted to detect the effect of parameter dependency,and demonstrates that on the fixed energy level and stiffness profile,the faster running speed with larger convergence rate of the stable fixed point under small local perturbation can be achieved via decreasing the angle of attack and increasing the stiffness coefficient.The perturbation recovery test is implemented to judge the ability of the model resisting large external disturbance.The result shows that the convex stiffness performs best in enhancing the robustness of SLIP runner negotiating irregular terrain.This research sheds light on the running performance of the SLIP runner with nonlinear leg spring from a theoretical perspective,and also guides the design and control of the bio-inspired legged robot.

Global Attraction in the Piecewise Rotation of the Sigma-Delta Modulator

This paper presents a complete proof of a conjecture given by Ashwin, Deane and Fu that the map describing the dynamical behavior of the Sigma-Delta modulator has a global attractor. By viewing the map as a piecewise rotation, and by geometric analysis, the authors give a simpler and more sufficient proof of the conjecture, than the one presented by Deane and published in Dynamical Systems, 2002,17： 377 - 388.

Nonlinear optimal control for robotic yoyo playing

A general approach for controlling of periodical dynamic systems was presented by taking robotic yoyo as an example. The height of the robot arm when the yoyo arrives at the bottom was chosen as virtual control. The initial amplitude of yoyo could be mapped to the desired final amplitude by adjusting the virtual control. First,the yoyo motion was formulated into a nonlinear optimal control problem which contained the virtual control. The reference trajectory of robot could be obtained by solving the optimal problem with analytic method or more general numerical approach. Then,both PI and deadbeat control methods were used to control the yoyo system. The simulation results show that the analytic solution of the reference trajectory is identical to the numerical solution,which mutually validates the correctness of the two solution methods. In simulation,the initial amplitude of yoyo is set to be 0.22 m which is 10% higher than the desired final amplitude of 0.2 m. It can be seen that the amplitude achieves the desired value asymptotically in about five periods when using PI control,while it needs only one period with deadbeat control. The reference trajectory of robot is generated by optimizing a certain performance index; therefore,it is globally optimal. This is essentially different from those traditional control methods,in which the reference trajectories are empirically imposed on robot. What's more,by choosing the height of the robot arm when the yoyo arrives at the bottom as the virtual control,the motion of the robot arm may not be out of its stroke limitation. The proposed approach may also be used in the control of other similar periodical dynamic systems.

ON THE DECISION PROBLEM OF THE CENTER OR FOCUS FOR A CLASS OF PLANAR POLYNOMIAL FIELDS

In this paper we study the decision problem of the center or focus for a class of planar polynomial fields which can be changed into Abel equation. Taking a Poincaré return map h(x) , we can calculate any order derivative of h(x) at x=0 and obtain the focus value of each order. The new method in this paper avoids the recurence operation and reduces the work in calculating the focus value.

Coupled solid-fluid FE-analysis of an embankment dam

A coupled solid-fluid FE-model for partially saturated soils,characterized by modeling the soil as a three-phase material consisting of a deformable soil skeleton and the fluid phases water and air,is reviewed briefly.As a constitutive model for the soil skeleton,the well-known Barcelona Basic model(BBM)is employed,which is formulated in terms of net stress and matric suction.For the BBM,a computationally efficient return mapping algorithm is proposed,which only requires the solution of a scalar nonlinear equation at the integration point level.The coupled FE-model is applied to the coupled transient numerical simulation of the water flow and the deformations and stresses in an embankment dam.

Approximate Perturbation Stance Map of the SLIP Runner and Application to Locomotion Control

This paper presents a novel method of perturbation to obtain the analytic approximate solution to the Spring-Loaded Inverted Pendulum （SLIP） dynamics in stance phase with considering the effect of gravity. This perturbation solution achieves higher accuracy in predicting the apex state variables than the typical existing analytic approximations. Particularly, our solution is validated for non-symmetric trajectory of hopping in a large angle range. Furthermore, the stance controller of the SLIP runner is developed to regulate the apex state based on the approximate apex return map. To compensate the energy variation between the current and desired apex states, a stiffness adjustment of the leg spring in stance phase is presented. The deadbeat controller of the angle of attack is designed to track the regulated apex height and velocity. The simulation demonstrates that the SLIP runner applying the proposed stance controller reveals higher tracking accuracy and more rapidly converges to the regulated apex state.

Nongeneric Bifurcations Near a Nontransversal Heterodimensional Cycle

In this paper bifurcations of heterodimensional cycles with highly degenerate conditions are studied in three dimensional vector fields,where a nontransversal intersection between the two-dimensional manifolds of the saddle equilibria occurs.By setting up local moving frame systems in some tubular neighborhood of unperturbed heterodimensional cycles,the authors construct a Poincar′e return map under the nongeneric conditions and further obtain the bifurcation equations.By means of the bifurcation equations,the authors show that different bifurcation surfaces exhibit variety and complexity of the bifurcation of degenerate heterodimensional cycles.Moreover,an example is given to show the existence of a nontransversal heterodimensional cycle with one orbit flip in three dimensional system.

A predictive model of death from cerebrovascular diseases in intensive care units

Objective This study aimed to explore the mortality prediction of patients with cerebrovascular diseases inthe intensive care unit(ICU)by examining the important signals during different periods of admission in theICU,which is considered one of the new topics in the medical field.Several approaches have been proposed forprediction in this area.Each of these methods has been able to predict mortality somewhat,but many of thesetechniques require recording a large amount of data from the patients,where recording all data is not possiblein most cases;at the same time,this study focused only on heart rate variability(HRV)and systolic and diastolicblood pressure.Methods The ICU data used for the challenge were extracted from the Multiparameter Intelligent Monitoring inIntensive Care II(MIMIC-II)Clinical Database.The proposed algorithm was evaluated using data from 88 cerebrovascular ICU patients,48 men and 40 women,during their first 48 hours of ICU stay.The electrocardiogram(ECG)signals are related to lead II,and the sampling frequency is 125 Hz.The time of admission and time ofdeath are labeled in all data.In this study,the mortality prediction in patients with cerebral ischemia is evaluated using the features extracted from the return map generated by the signal of HRV and blood pressure.Topredict the patient’s future condition,the combination of features extracted from the return mapping generatedby the HRV signal,such as angle(𝛼),area(A),and various parameters generated by systolic and diastolic bloodpressure,including DBPMax−Min SBPSD have been used.Also,to select the best feature combination,the geneticalgorithm(GA)and mutual information(MI)methods were used.Paired sample t-test statistical analysis was usedto compare the results of two episodes(death and non-death episodes).The P-value for detecting the significancelevel was considered less than 0.005.Results The results indicate that the new approach presented in this paper can be compared with other methodsor leads to better results.The best combination of features based on GA to achieve maximum predictive accuracywas m(mean),L_(Mean),A,SBP_(SVMax),DBP_(Max-Min).The accuracy,specificity,and sensitivity based on the best featuresobtained from GA were 97.7%,98.9%,and 95.4%for cerebral ischemia disease with a prediction horizon of0.5–1 hour before death.The d-factor for the best feature combination based on the GA model is less than 1(d-factor=0.95).Also,the bracketed by 95 percent prediction uncertainty(95PPU)(%)was obtained at 98.6.Conclusion The combination of HRV and blood pressure signals might increase the accuracy of the predictionof the death episode and reduce the minimum hospitalization time of the patient with cerebrovascular diseasesto determine the future status.

A NOTE ON THE STABILITY OF A CLASS OF DEGENERATE PLANAR CRITICAL POINTS

A computable expression of the asymptotic expansion of the return map for a degenerate singular point of a class of planar differential system is given, and hence the stability and the type of the singular point can be decided. These results generalize the corresponding results in [Nonlinearity, 13 （2000）, p.709].

Sagittal SLIP-anchored task space control for a monopode robot traversing irregular terrain

As a well-explored template that captures the essential dynamical behaviors of legged locomotion on sagittal plane,the spring-loaded inverted pendulum(SLIP)model has been extensively employed in both biomechanical study and robotics research.Aiming at fully leveraging the merits of the SLIP model to generate the adaptive trajectories of the center of mass(CoM)with maneuverability,this study presents a novel two-layered sagittal SLIP-anchored(SSA)task space control for a monopode robot to deal with terrain irregularity.This work begins with an analytical investigation of sagittal SLIP dynamics by deriving an approximate solution with satisfactory apex prediction accuracy,and a two-layered SSA task space controller is subsequently developed for the monopode robot.The higher layer employs an analytical approximate representation of the sagittal SLIP model to form a deadbeat controller,which generates an adaptive reference trajectory for the CoM.The lower layer enforces the monopode robot to reproduce a generated CoM movement by using a task space controller to transfer the reference CoM commands into joint torques of the multi-degree of freedom monopode robot.Consequently,an adaptive hopping behavior is exhibited by the robot when traversing irregular terrain.Simulation results have demonstrated the effectiveness of the proposed method.