scholarly journals STATIONARY SOLUTIONS TO FOREST KINEMATIC MODEL

2009 ◽  
Vol 51 (1) ◽  
pp. 1-17 ◽  
Author(s):  
LE HUY CHUAN ◽  
TOHRU TSUJIKAWA ◽  
ATSUSHI YAGI
Keyword(s):  
Dynamical System ◽  
Mathematical Model ◽  
Infinite Number ◽  
Kinematic Model ◽  
Stationary Solutions ◽  
Cross Diffusion ◽  
Stability And Instability ◽  
Math Biol ◽  
Forest Boundary ◽  
Boundary Dynamics

AbstractWe continue the study of a mathematical model for a forest ecosystem which has been presented by Y. A. Kuznetsov, M. Y. Antonovsky, V. N. Biktashev and A. Aponina (A cross-diffusion model of forest boundary dynamics, J. Math. Biol. 32 (1994), 219–232). In the preceding two papers (L. H. Chuan and A. Yagi, Dynamical systemfor forest kinematic model, Adv. Math. Sci. Appl. 16 (2006), 393–409; L. H. Chuan, T. Tsujikawa and A. Yagi, Aysmptotic behavior of solutions for forest kinematic model, Funkcial. Ekvac. 49 (2006), 427–449), the present authors already constructed a dynamical system and investigated asymptotic behaviour of trajectories of the dynamical system. This paper is then devoted to studying not only the structure (including stability and instability) of homogeneous stationary solutions but also the existence of inhomogeneous stationary solutions. Especially it shall be shown that in some cases, one can construct an infinite number of discontinuous stationary solutions.

A cross-diffusion model of forest boundary dynamics

1994 ◽  
Vol 32 (3) ◽  
pp. 219-232 ◽  
Author(s):  
Yu. A. Kuznetsov ◽  
M. Ya. Antonovsky ◽  
V. N. Biktashev ◽  
E. A. Aponina
Keyword(s):  
Diffusion Model ◽  
Cross Diffusion ◽  
Forest Boundary ◽  
Boundary Dynamics

A DYNAMICAL SYSTEM WITH CHAOTIC BEHAVIOR

1989 ◽  
Vol 03 (15) ◽  
pp. 1185-1188 ◽  
Author(s):  
J. SEIMENIS
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Infinite Number ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Hamiltonian Dynamical Systems

We develop a method to find solutions of the equations of motion in Hamiltonian Dynamical Systems. We apply this method to the system [Formula: see text] We study the case a → 0 and we find that in this case the system has an infinite number of period dubling bifurcations.

scholarly journals MODELING OF THE SPINE COMPENSATORY RESPONSE TO DEFORMITY

2018 ◽  
Vol 15 (3) ◽  
pp. 85-91
Author(s):  
A. V. Krutko ◽  
A. V. Gladkov ◽  
V. V. Komissarov ◽  
N. V. Komissarova
Keyword(s):  
Mathematical Model ◽  
Center Of Mass ◽  
Kinematic Model ◽  
Sagittal Imbalance ◽  
Spine Deformity ◽  
Compensatory Mechanism ◽  
Spinal Deformities ◽  
Compensatory Response ◽  
The Mathematical Model ◽  
Pathological Situation

Objective. To analyze mathematical model of the efficiency of the compensatory mechanism of the deformed spine. Material and Methods. The developed basic kinematic model of the spine was used. The restoration of the position of the projection of the general center of mass (GCM) was mathematically modeled, and mechanogenesis of the spinal deformity and possibility of its compensation were evaluated. To assess the reliability of the mathematical model, spinal skiagrams taken from patients with clinically confirmed pathology and sagittal imbalance were used. Results. On the basis of quantitative characteristics of the primary spine deformity of a certain clinical case and using the developed algorithm, it is possible to create a model of both a primary deformity and a compensatory response from intact segments of the spine taking into account the influencing factors. This makes it possible to use the proposed kinematic model in scientific research on predicting the course of various types of spinal deformities. Conclusion. The proposed algorithms simulating the development of spinal deformities based on the restoration of the position of the GCM projection reflect their mechanogenesis and can be used to model various pathological conditions of the spine. A complete correction of the deformity does not mean a complete cure, since the required spinal fusion creates a new, prognostically less significant, but pathological situation.

scholarly journals Analysis of the Strong and Weak Monotonic External Stability of the Resonance in a Perturbed Dynamical System

2021 ◽  
Vol 16 ◽  
pp. 180-191
Author(s):  
Vladislav V. Lyubimov
Keyword(s):  
Dynamical System ◽  
Sufficient Conditions ◽  
Strong Stability ◽  
New Classification ◽  
External Stability ◽  
Fast Phase ◽  
Stability And Instability ◽  
Long Time ◽  
Independent Variable

A perturbed dynamical system involving two ordinary differential equations is under review. Whereupon, the differential equation for determining the fast phase contains the ratio of the two frequencies. When these frequencies coincide for a long time, a resonance is implemented in this system. The aim of this paper is to obtain the conditions of monotonic external stability and instability of this resonance. The sufficient conditions for the external stability and instability of the resonance defined in this paper assume that the signs of the analyzed derivatives remain unchanged in the non-resonant section of the change in the independent variable. This paper gives a new classification of the phenomenon of external stability of resonance, which includes weak, linear, and strong stability. It should be noted that the conditions of monotonic external stability and instability of the resonance presented in this paper can be used in various scientific and technological problems, in which resonances are observed. Particularly, the concluding part of the paper considers the application of the results obtained within the framework of the problem of the perturbed motion of a rigid body relative to a fixed point.

Geometry and Kinematics of Cylindrical Waterbomb Tessellation

2021 ◽  
Author(s):  
Rinki Imada ◽  
Tomohiro Tachi
Keyword(s):  
Dynamical System ◽  
Recurrence Relation ◽  
Discrete Dynamical System ◽  
Kinematic Model ◽  
Theoretical Reason ◽  
Finite Solution ◽  
Geometry And Kinematics ◽  
Folded Surfaces

Abstract Folded surfaces of origami tessellations have attracted much attention because they sometimes exhibit non-trivial behaviors. It is known that cylindrical folded surfaces of waterbomb tessellation called waterbomb tube can transform into wave-like surfaces, which is a unique phenomenon not observed on other tessellations. However, the theoretical reason why wave-like surfaces arise has been unclear. In this paper, we provide a kinematic model of waterbomb tube by parameterizing the geometry of a module of waterbomb tessellation and derive a recurrence relation between the modules. Through the visualization of the configurations of waterbomb tubes under the proposed kinematic model, we classify solutions into three classes: cylinder solution, wave-like solution, and finite solution. Furthermore, we give proof of the existence of a wave-like solution around one of the cylinder solutions by applying the knowledge of the discrete dynamical system to the recurrence relation.

Simulation of frequency dependence of compliance and resistance in healthy man

1975 ◽  
Vol 38 (3) ◽  
pp. 427-435 ◽  
Author(s):  
H. Bobbaers ◽  
J. Clement ◽  
J. Pardaens ◽  
K. P. Woestijne
Keyword(s):  
Mechanical Properties ◽  
Mathematical Model ◽  
Frequency Dependence ◽  
Infinite Number ◽  
Pressure Difference ◽  
Healthy Adult ◽  
Lung Parenchyma ◽  
Pleural Pressure ◽  
Bronchial Wall ◽  
Sinusoidal Input

The frequency dependence of effective compliance, Ceff, and resistance, Reff, are reproduced by means of a two- or four-compartment linear mathematical model with pleural pressure as a sinusoidal input. The model simulates the mechanical properties of lung parenchyma, alveolar gas, bronchial wall, and cheeks, as well as the distribution of gaseous resistances and inertances within the airways. Values, representative for a young healthy adult, are assigned to these various parametersmit appears from this study: 1) that the gas inertance produces a very marked increase of Ceff, noticeable already below 1 cycle/smto obtain a frequency independence of Ceff between 0 and 2 cycles/s, it is necessary to introduce a marked inhomogeneity in the model. 2) Such an inhomogeneity is realized by simulating a pleural pressure difference of 6 cmH2O between the compartments of the bialveolar model. It can be shown that this corresponds to a total pleural pressure difference of about 9 cmH2O in a model consisting of an infinite number of compartments. 3) The influence of the compressibility of alveolar gas and of mechanical properties of the bronchial wall and of the cheeks on Ceff and Reff is small or negligible.

Modeling and prototyping of a soft closed-chain modular gripper

2019 ◽  
Vol 46 (1) ◽  
pp. 135-145 ◽  
Author(s):  
Muddasar Anwar ◽  
Toufik Al Khawli ◽  
Irfan Hussain ◽  
Dongming Gan ◽  
Federico Renda
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Chain Structure ◽  
Mathematical Representation ◽  
Mathematical Framework ◽  
Complex Objects ◽  
Content Type ◽  
Design And Optimization ◽  
Closed Chain

Purpose This paper aims to present a soft closed-chain modular gripper for robotic pick-and-place applications. The proposed biomimetic gripper design is inspired by the Fin Ray effect, derived from fish fins physiology. It is composed of three axisymmetric fingers, actuated with a single actuator. Each finger has a modular under-actuated closed-chain structure. The finger structure is compliant in contact normal direction, with stiff crossbeams reorienting to help the finger structure conform around objects. Design/methodology/approach Starting with the design and development of the proposed gripper, a consequent mathematical representation consisting of closed-chain forward and inverse kinematics is detailed. The proposed mathematical framework is validated through the finite element modeling simulations. Additionally, a set of experiments was conducted to compare the simulated and prototype finger trajectories, as well as to assess qualitative grasping ability. Findings Key Findings are the presented mathematical model for closed-loop chain mechanisms, as well as design and optimization guidelines to develop controlled closed-chain grippers. Research limitations/implications The proposed methodology and mathematical model could be taken as a fundamental modular base block to explore similar distributed degrees of freedom (DOF) closed-chain manipulators and grippers. The enhanced kinematic model contributes to optimized dynamics and control of soft closed-chain grasping mechanisms. Practical implications The approach is aimed to improve the development of soft grippers that are required to grasp complex objects found in human–robot cooperation and collaborative robot (cobot) applications. Originality/value The proposed closed-chain mathematical framework is based on distributed DOFs instead of the conventional lumped joint approach. This is to better optimize and understand the kinematics of soft robotic mechanisms.

Eigenvalue problems for the wave equation with strong damping

1997 ◽  
Vol 127 (4) ◽  
pp. 755-771 ◽  
Author(s):  
Pedro Freitas
Keyword(s):  
Stationary Solution ◽  
Wave Equations ◽  
Eigenvalue Problems ◽  
Sufficient Conditions ◽  
Stationary Solutions ◽  
Linear Operators ◽  
Stability And Instability ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Strongly Damped

This paper presents a study of linear operators associated with the linearisation of general semilinear strongly damped wave equations around stationary solutions. The structure of the spectrum of such operators is considered in detail, with an emphasis on stability questions. Necessary and sufficient conditions for the stability of the trivial solution of the linear equation are given, together with conditions for this solution to become unstable. In the latter case, the mechanisms which are responsible for the change of stability are analysed. These results are then applied to obtain stability and instability conditions for the semilinear problem. In particular, a condition is given which ensures that the dimensions of the centre and unstable manifolds of a stationary solution are the same as when that solution is considered as a stationary solution of an associated parabolic problem.

Fuzzy Approximation by a Novel Levenberg–Marquardt Method for Two-Degree-of-Freedom Hypersonic Flutter Model

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Y. H. Wang ◽  
L. Zhu ◽  
Q. X. Wu ◽  
C. S. Jiang
Keyword(s):  
Dynamical System ◽  
Mathematical Model ◽  
Approximation Scheme ◽  
Degree Of Freedom ◽  
Human Knowledge ◽  
Marquardt Method ◽  
Fuzzy Approximation ◽  
Levenberg Marquardt ◽  
Modification Factor ◽  
Two Degree Of Freedom

The two-degree-of-freedom (2DOF) hypersonic flutter dynamical system has strong aeroelastic nonlinearities, and it is very difficult to obtain a more precise mathematical model. By considering varying learning rate and σ-modification factor, a novel Levenberg– Marquardt (L–M) method is proposed, based on which, an online fuzzy approximation scheme for 2DOF hypersonic flutter model is established without any human knowledge. Compared with the standard L–M method, the proposed method can obtain faster converge speed and avoid parameter drift. Numerical simulations approve the advantages of the proposed scheme.

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