scholarly journals Hip retraction enhances walking stability on a ramp: an equilibrium point hypothesis-based study

2019 ◽  
Author(s):  
Alireza Bahramian ◽  
Elham Shamsi ◽  
Farzad Towhidkhah ◽  
Sajad Jafari
Keyword(s):  
Equilibrium Point ◽  
Equilibrium Points ◽  
Human Motion ◽  
Body Motion ◽  
Equilibrium Point Hypothesis ◽  
The Central Nervous System ◽  
Natural Response ◽  
External Forces ◽  
Positive Effect ◽  
Body Joint

AbstractHip retraction is a phenomenon observed in human walking. The swing leg rotates backward at the end of the motion. Its positive effect on motion stability was reported in the literature based on some simple models for running or walking. In this study, it is shown that hip retraction angle increases in humans during their ascending and descending walk on a stair. In previous studies, hip retraction was modeled by defining a proper motion for the swing leg. According to the equilibrium point hypothesis, the central nervous system (CNS) defines only the equilibrium point(s) and stiffness(es) for body joint(s) to control the human motion. Human body motion emerges as its natural response as a result of the external forces and the defined equilibrium points of joints. Considering the hip torque as a spring-like model with an equilibrium point and stiffness, this study revealed that the hip retraction can be generated by the natural response of the swing leg. Besides, the stabilizing effect of hip retraction was demonstrated by a model for human’s ascending and descending walking on a ramp with a range of positive and negative angles, respectively. The findings suggest that the CNS needs to define equilibrium point just ahead of the stance leg to take advantage of the hip retraction effect on ascending and descending walks on a ramp.

scholarly journals Dynamics of an Eco-Epidemic Predator–Prey Model Involving Fractional Derivatives with Power-Law and Mittag–Leffler Kernel

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 785
Author(s):  
Hasan S. Panigoro ◽  
Agus Suryanto ◽  
Wuryansari Muharini Kusumawinahyu ◽  
Isnani Darti
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Derivative ◽  
Equilibrium Point ◽  
Power Law ◽  
Equilibrium Points ◽  
Essential Difference ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Infected Prey

In this paper, we consider a fractional-order eco-epidemic model based on the Rosenzweig–MacArthur predator–prey model. The model is derived by assuming that the prey may be infected by a disease. In order to take the memory effect into account, we apply two fractional differential operators, namely the Caputo fractional derivative (operator with power-law kernel) and the Atangana–Baleanu fractional derivative in the Caputo (ABC) sense (operator with Mittag–Leffler kernel). We take the same order of the fractional derivative in all equations for both senses to maintain the symmetry aspect. The existence and uniqueness of solutions of both eco-epidemic models (i.e., in the Caputo sense and in ABC sense) are established. Both models have the same equilibrium points, namely the trivial (origin) equilibrium point, the extinction of infected prey and predator point, the infected prey free point, the predator-free point and the co-existence point. For a model in the Caputo sense, we also show the non-negativity and boundedness of solution, perform the local and global stability analysis and establish the conditions for the existence of Hopf bifurcation. It is found that the trivial equilibrium point is a saddle point while other equilibrium points are conditionally asymptotically stable. The numerical simulations show that the solutions of the model in the Caputo sense strongly agree with analytical results. Furthermore, it is indicated numerically that the model in the ABC sense has quite similar dynamics as the model in the Caputo sense. The essential difference between the two models is the convergence rate to reach the stable equilibrium point. When a Hopf bifurcation occurs, the bifurcation points and the diameter of the limit cycles of both models are different. Moreover, we also observe a bistability phenomenon which disappears via Hopf bifurcation.

scholarly journals Research of Trajectory Optimization Approaches in Synthesized Optimal Control

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 336
Author(s):  
Askhat Diveev ◽  
Elizaveta Shmalko
Keyword(s):  
Optimal Control ◽  
Equilibrium Point ◽  
Trajectory Optimization ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Control Object ◽  
Symbolic Regression ◽  
Optimal Location ◽  
Stable Equilibrium Point ◽  
Stabilization System

This article presents a study devoted to the emerging method of synthesized optimal control. This is a new type of control based on changing the position of a stable equilibrium point. The object stabilization system forces the object to move towards the equilibrium point, and by changing its position over time, it is possible to bring the object to the desired terminal state with the optimal value of the quality criterion. The implementation of such control requires the construction of two control contours. The first contour ensures the stability of the control object relative to some point in the state space. Methods of symbolic regression are applied for numerical synthesis of a stabilization system. The second contour provides optimal control of the stable equilibrium point position. The present paper provides a study of various approaches to find the optimal location of equilibrium points. A new problem statement with the search of function for optimal location of the equilibrium points in the second stage of the synthesized optimal control approach is formulated. Symbolic regression methods of solving the stated problem are discussed. In the presented numerical example, a piece-wise linear function is applied to approximate the location of equilibrium points.

scholarly journals Elastic Simulation of Joints with Particle-Based Fluid

2021 ◽  
Vol 11 (15) ◽  
pp. 6900
Author(s):  
Su-Kyung Sung ◽  
Sang-Won Han ◽  
Byeong-Seok Shin
Keyword(s):  
Principal Stress ◽  
Human Body ◽  
Yield Condition ◽  
Maximum Principal Stress ◽  
Human Motion ◽  
The Difference ◽  
The Moment ◽  
External Forces ◽  
Physical Changes ◽  
Elastic Simulation

Skinning, which is used in skeletal simulations to express the human body, has been weighted between bones to enable muscle-like motions. Weighting is not a form of calculating the pressure and density of muscle fibers in the human body. Therefore, it is not possible to express physical changes when external forces are applied. To express a similar behavior, an animator arbitrarily customizes the weight values. In this study, we apply the kernel and pressure-dependent density variations used in particle-based fluid simulations to skinning simulations. As a result, surface tension and elasticity between particles are applied to muscles, indicating realistic human motion. We also propose a tension yield condition that reflects Tresca’s yield condition, which can be easily approximated using the difference between the maximum and minimum values of the principal stress to simulate the tension limit of the muscle fiber. The density received by particles in the kernel is assumed to be the principal stress. The difference is calculated by approximating the moment of greatest force to the maximum principal stress and the moment of least force to the minimum principal stress. When the density of a particle increases beyond the yield condition, the object is no longer subjected to force. As a result, one can express realistic muscles.

scholarly journals Synergies in the space of control variables within the equilibrium-point hypothesis

Neuroscience ◽  
2016 ◽  
Vol 315 ◽  
pp. 150-161 ◽  
Author(s):  
S. Ambike ◽  
D. Mattos ◽  
V.M. Zatsiorsky ◽  
M.L. Latash
Keyword(s):  
Equilibrium Point ◽  
Control Variables ◽  
Equilibrium Point Hypothesis

scholarly journals Analysis of Smooth Implementation of Industry Poverty Alleviation considering Government Supervision

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Haifeng Yao ◽  
Jiangyue Fu
Keyword(s):  
Equilibrium Point ◽  
Evolutionary Game Theory ◽  
Poverty Alleviation ◽  
Equilibrium Points ◽  
Evolutionary Game ◽  
Parameter Design ◽  
Game Model ◽  
Government Supervision ◽  
Proposed Model ◽  
The Government

Vigorous implementation of industrial poverty alleviation is the fundamental path and core power of poverty alleviation in impoverished areas. Enterprises and poor farmers are the main participants in industry poverty alleviation. Government supervision measures regulate their behaviors. This study investigates how to smoothly implement industry poverty alleviation projects considering government supervision. A game model is proposed based on the evolutionary game theory. It analyses the game processes between enterprises and poor farmers with and without government supervision based on the proposed model. It is shown that poverty alleviation projects will fail without government supervision given that the equilibrium point (0, 0) is the ultimate convergent point of the system but will possibly succeed with government supervision since the equilibrium points (0, 0) and (1, 1) are the ultimate convergent point of the system, where equilibrium point (1, 1) is our desired results. Different supervision modes have different effects on the game process. This study considers three supervision modes, namely, only reward mode, only penalty mode, and reward and penalty mode, and investigates the parameter design for the reward and penalty mode. The obtained results are helpful for the government to develop appropriate policies for the smooth implementation of industry poverty alleviation projects.

scholarly journals PENGEMBANGAN MODEL EPIDEMIK SIRA UNTUK PENYEBARAN VIRUS PADA JARINGAN KOMPUTER

2019 ◽  
Vol 2 (1) ◽  
pp. 13
Author(s):  
Panca Putra Pemungkas ◽  
Sutrisno Sutrisno ◽  
Sunarsih Sunarsih
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Computer Network ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Virus Spread ◽  
Computer Based ◽  
Stability Issues ◽  
Spread Analysis

This paper is addressed to discuss the development of epidemic model of SIRA (Susceptible-Infected-Removed-Antidotal) for virus spread analysis purposes on a computer network. We have developed the existing model by adding a possibility of antidotal computer returned to susceptible computer. Based on the results, there are two virus-free equilibrium points and one endemic equilibrium point. These equilibrium points were analyzed for stability issues using basic reproduction number and Routh-Hurwitz Method.

scholarly journals A Stage-Structure Rosenzweig-MacArthur Model with Effect of Prey Refuge

2020 ◽  
Vol 1 (1) ◽  
pp. 1-7
Author(s):  
Lazarus Kalvein Beay ◽  
Maryone Saija
Keyword(s):  
Equilibrium Point ◽  
Local Stability ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Structure Population ◽  
Prey Refuge ◽  
Behavioral System ◽  
Trivial Equilibrium ◽  
Coexistence Equilibrium

We proposed and analyzed a stage-structure Rosenzweig-MacArthur model incorporating a prey refuge.  It is assumed that the prey is a stage-structure population consisting of two compartments known as immature prey and mature prey. The model incorporates the functional response Holling type-II. In this work, we investigate all the biologically feasible equilibrium points, and it is shown that the system has three equilibrium points. Sufficient conditions for the local stability of the non-negative equilibrium point of the model are also derived. All points are conditionally locally asymptotically stable. By constructing Jacobian matrix and determined eigenvalues, we analyzed the local stability of the trivial equilibrium and non-predator equilibrium points. Specifically for coexistence equilibrium point, Routh-Hurwitz criterion used to analyze local stability. In addtion, we investigated the effect of immature prey refuge. Our mathematical analysis exhibits that immature prey refuge have played a crucial role in the behavioral system. When the effect of immature prey refuge (constant m) increases, it is can stabilize non-predator equilibrium point, where all the species can not exists together. And conversely, if contant m decreases, it is can stabilize coexistence equilibrium point then all the species can exists together. The work is completed with a numerical simulation to confirmed analitical results

scholarly journals Mathematical Modelling of Deforestation Due to Population Density and Industrialization

Jurnal Varian ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 9-16
Author(s):  
Didiharyono D. ◽  
Irwan Kasse
Keyword(s):  
Numerical Simulation ◽  
Population Density ◽  
Mathematical Modelling ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Stability Criteria ◽  
Hurwitz Stability ◽  
Stable Conditions ◽  
Linear Differential ◽  
The Stability

The focus of the study in this paper is to model deforestation due to population density and industrialization. To begin with, it is formulated into a mathematical modelling which is a system of non-linear differential equations. Then, analyze the stability of the system based on the Routh-Hurwitz stability criteria. Furthermore, a numerical simulation is performed to determine the shift of a system. The results of the analysis to shown that there are seven non-negative equilibrium points, which in general consist equilibrium point of disturbance-free and equilibrium points of disturbances. Equilibrium point TE7(x, y, z) analyzed to shown asymptotically stable conditions based on the Routh-Hurwitz stability criteria. The numerical simulation results show that if the stability conditions of a system have been met, the system movement always occurs around the equilibrium point.

scholarly journals Sonifying the Shape of Human Body Motion using Motiongrams

2013 ◽  
Vol 8 (2) ◽  
pp. 73 ◽  
Author(s):  
Alexander Refsum Jensenius ◽  
Rolf Inge Godøy
Keyword(s):  
Human Body ◽  
Video Recording ◽  
Visual Display ◽  
Human Motion ◽  
Visual Similarity ◽  
Body Motion ◽  
Auditory Displays ◽  
Musical Sound ◽  
Starting Point ◽  
Spatial Shape

<p class="author">The paper presents sonomotiongram, a technique for the creation of auditory displays of human body motion based on motiongrams. A motiongram is a visual display of motion, based on frame differencing and reduction of a regular video recording. The resultant motiongram shows the spatial shape of the motion as it unfolds in time, somewhat similar to the way in which spectrograms visualise the shape of (musical) sound. The visual similarity of motiongrams and spectrograms is the conceptual starting point for the sonomotiongram technique, which explores how motiongrams can be turned into sound using &ldquo;inverse FFT&rdquo;. The paper presents the idea of shape-sonification, gives an overview of the sonomotiongram technique, and discusses sonification examples of both simple and complex human motion.</p>

Dynamics of an ecological system

2019 ◽  
Vol 10 (4) ◽  
pp. 355-376
Author(s):  
Shashi Kant
Keyword(s):  
Saddle Point ◽  
Numerical Simulations ◽  
Equilibrium Point ◽  
Local Stability ◽  
Deterministic Model ◽  
Equilibrium Points ◽  
Prey Refuge ◽  
Trivial Equilibrium ◽  
Stability Results ◽  
Predator System

AbstractIn this paper, we investigate the deterministic and stochastic prey-predator system with refuge. The basic local stability results for the deterministic model have been performed. It is found that all the equilibrium points except the positive coexisting equilibrium point of the deterministic model are independent of the prey refuge. The trivial equilibrium point, predator free equilibrium point and prey free equilibrium point are always unstable (saddle point). The existence and local stability of the coexisting equilibrium point is related to the prey refuge. The permanence and extinction conditions of the proposed biological model have been studied rigourously. It is observed that the stochastic effect may be seen in the form of decaying of the species. The numerical simulations for different values of the refuge values have also been included for understanding the behavior of the model graphically.

Sign in / Sign up

Export Citation Format

Share Document