The transition from a periodic spiking state to a periodic bursting state via a chaotic bursting state: a numerical study of a dynamical system in neurobiophysics

2020 ◽  
Vol 14 (4) ◽  
pp. 151-160
Author(s):  
Takaaki Shirahata
Keyword(s):  
Dynamical System ◽  
Numerical Study ◽  
Chaotic Bursting

DYNAMICS AT INFINITY OF A CUBIC CHUA'S SYSTEM

2011 ◽  
Vol 21 (01) ◽  
pp. 333-340 ◽  
Author(s):  
MARCELO MESSIAS
Keyword(s):  
Dynamical System ◽  
Vector Field ◽  
Numerical Study ◽  
Three Dimensional ◽  
Polynomial Vector ◽  
Cubic Nonlinearity ◽  
Poincaré Compactification ◽  
Global Study ◽  
Dimensional Dynamical System ◽  
Parameter Values

We use the Poincaré compactification for a polynomial vector field in ℝ3 to study the dynamics near and at infinity of the classical Chua's system with a cubic nonlinearity. We give a complete description of the phase portrait of this system at infinity, which is identified with the sphere 𝕊2 in ℝ3 after compactification, and perform a numerical study on how the solutions reach infinity, depending on the parameter values. With this global study we intend to give a contribution in the understanding of this well known and extensively studied complex three-dimensional dynamical system.

scholarly journals Numerical study for fractional model of non-linear predator-prey biological population dynamical system

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 2017-2025 ◽  
Author(s):  
Jagdev Singh ◽  
Adem Kilicman ◽  
Devendra Kumar ◽  
Ram Swroop ◽  
Fadzilah Ali
Keyword(s):  
Dynamical System ◽  
Population Model ◽  
Numerical Scheme ◽  
Series Solution ◽  
Numerical Study ◽  
Computational Approach ◽  
Predator Prey ◽  
Biological Population ◽  
Non Linear ◽  
Homotopy Analysis

The key objective of the present paper is to propose a numerical scheme based on the homotopy analysis transform technique to analyze a time-fractional non-linear predator-prey population model. The population model are coupled fractional order non-linear PDE often employed to narrate the dynamics of biological systems in which two species interact, first is a predator and the second is a prey. The proposed scheme provides the series solution with a great freedom and flexibility by choosing appropriate parameters. The convergence of the results is free from small or large parameters. Three examples are discussed to demonstrate the correctness and efficiency of the used computational approach.

A Consistent, Hybrid-Dynamical-System, Lumped-Parameter Model of Tire–Terrain Interactions

2015 ◽  
Vol 10 (3) ◽  
Author(s):  
Pravesh Sanghvi ◽  
Harry Dankowicz
Keyword(s):  
Dynamical System ◽  
Shear Failure ◽  
Internal State ◽  
Numerical Study ◽  
Lumped Parameter Model ◽  
State Variables ◽  
Hybrid Dynamical System ◽  
Steady State Condition ◽  
Internal State Variables ◽  
Lumped Parameter

This paper establishes the internal mathematical and energetic consistency of a hybrid-dynamical-system, lumped-parameter, planar, physical model for capturing transient interactions between an elastically deformable tire and an elastically deformable terrain as a baseline result for more realistic models that account for permanent deformation, shear failure, and three-dimensional contact conditions. The model accounts for radial and circumferential deformation of the tire as well as normal and tangential deformation of the terrain. It captures the onset and loss of contact as well as localized stick and slip phases for each of the discrete tire elements by a suitable evolution of a collection of associated internal state variables. The analysis characterizes generic transitions between distinct phases of contact uniquely in forward time and proves that all internal state variables remain bounded during compact intervals of contact. The behavior of the model is further illustrated through an analytical and numerical study of two instances of tire-terrain interactions under steady state condition.

scholarly journals Dynamical properties of spatial discretizations of a generic homeomorphism

2014 ◽  
Vol 35 (5) ◽  
pp. 1474-1523 ◽  
Author(s):  
PIERRE-ANTOINE GUIHÉNEUF
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Numerical Simulations ◽  
Numerical Study ◽  
Periodic Points ◽  
Dynamical Behaviour ◽  
Compact Manifolds ◽  
Spatial Discretization ◽  
Dynamical Features ◽  
Dynamical Properties

This paper concerns the link between the dynamical behaviour of a dynamical system and the dynamical behaviour of its numerical simulations. Here, we model numerical truncation as a spatial discretization of the system. Some previous works on well-chosen examples (such as Gambaudo and Tresser [Some difficulties generated by small sinks in the numerical study of dynamical systems: two examples. Phys. Lett. A 94(9) (1983), 412–414]) show that the dynamical behaviours of dynamical systems and of their discretizations can be quite different. We are interested in generic homeomorphisms of compact manifolds. So our aim is to tackle the following question: can the dynamical properties of a generic homeomorphism be detected on the spatial discretizations of this homeomorphism? We will prove that the dynamics of a single discretization of a generic conservative homeomorphism does not depend on the homeomorphism itself, but rather on the grid used for the discretization. Therefore, dynamical properties of a given generic conservative homeomorphism cannot be detected using a single discretization. Nevertheless, we will also prove that some dynamical features of a generic conservative homeomorphism (such as the set of the periods of all periodic points) can be read on a sequence of finer and finer discretizations.

scholarly journals A Constructive Method for Computing Generalized Manley-Rowe Constants of Motion

2013 ◽  
Vol 14 (4) ◽  
pp. 1094-1102
Author(s):  
Elena Kartashova ◽  
Loredana Tec
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Conservation Laws ◽  
Time Evolution ◽  
Numerical Study ◽  
Constructive Method ◽  
Constants Of Motion

AbstractThe Manley-Rowe constants of motion (MRC) are conservation laws written out for a dynamical system describing the time evolution of the amplitudes in resonant triad. In this paper we extend the concept of MRC to resonance clusters of any form yielding generalized Manley-Rowe constants (gMRC) and give a constructive method how to compute them. We also give details of a Mathematica implementation of this method. While MRC provide integrability of the underlying dynamical system, gMRC generally do not but may be used for qualitative and numerical study of dynamical systems describing generic resonance clusters.

Numerical study of the low-frequency atomic dynamics in a Lennard-Jones glass

1998 ◽  
Vol 77 (2) ◽  
pp. 473-484 ◽  
Author(s):  
M. Sampoli, P. Benassi, R. Dell'Anna,
Keyword(s):  
Numerical Study ◽  
Low Frequency ◽  
Lennard Jones
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