Numerical simulations of the dynamical behavior of the SK model

The nonlinear dynamics are studied for a supported cylinder subjected to axial flow. A nonlinear model is presented for dynamics of the cylinder supported at both ends. The nonlinear terms considered here are the quadratic viscous force and the structural nonlinear force induced by the lateral motions of the cylinder. Using two-mode discretized equation, numerical simulations are carried out for the dynamical behavior of the cylinder to explain the flutter instability found in the experiment. The results of numerical analysis show that at certain value of flow velocity the system loses stability by divergence, and the new equilibrium (the buckled configuration) becomes unstable at higher flow leading to post-divergence flutter. The effect of the friction drag coefficients on the behavior of the system is investigated.

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Optimal Synchronization of a Memristive Chaotic Circuit

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127416500930 ◽

2016 ◽

Vol 26 (06) ◽

pp. 1650093 ◽

Cited By ~ 7

Author(s):

Michaux Kountchou ◽

Patrick Louodop ◽

Samuel Bowong ◽

Hilaire Fotsin ◽

Jurgen Kurths

Keyword(s):

Numerical Simulations ◽

Chaos Synchronization ◽

Chaotic Systems ◽

Analog Circuit ◽

Electronic Circuit ◽

Dynamical Behavior ◽

Circuit Implementation ◽

Chaotic Circuit ◽

Dynamical Properties ◽

Analog Circuit Implementation

This paper deals with the problem of optimal synchronization of two identical memristive chaotic systems. We first study some basic dynamical properties and behaviors of a memristor oscillator with a simple topology. An electronic circuit (analog simulator) is proposed to investigate the dynamical behavior of the system. An optimal synchronization strategy based on the controllability functions method with a mixed cost functional is investigated. A finite horizon is explicitly computed such that the chaos synchronization is achieved at an established time. Numerical simulations are presented to verify the effectiveness of the proposed synchronization strategy. Pspice analog circuit implementation of the complete master-slave-controller systems is also presented to show the feasibility of the proposed scheme.

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DYNAMICS OF A PREY-DEPENDENT DIGESTIVE MODEL WITH STATE-DEPENDENT IMPULSIVE CONTROL

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127412500927 ◽

2012 ◽

Vol 22 (04) ◽

pp. 1250092 ◽

Cited By ~ 3

Author(s):

LINNING QIAN ◽

QISHAO LU ◽

JIARU BAI ◽

ZHAOSHENG FENG

Keyword(s):

Numerical Simulations ◽

Analytical Method ◽

Impulsive Control ◽

Dynamical Behavior ◽

Sufficient Conditions ◽

Period Doubling ◽

Lambert W Function ◽

Impulsive Effect ◽

State Dependent ◽

Theoretical Results

In this paper, we study the dynamical behavior of a prey-dependent digestive model with a state-dependent impulsive effect. Using the Poincaré map and the Lambert W-function, we find the analytical expression of discrete mapping. Sufficient conditions are established for transcritical bifurcation and period-doubling bifurcation through an analytical method. Exact locations of these bifurcations are explored. Numerical simulations of an example are illustrated which agree well with our theoretical results.

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6.5. Hydrodynamical simulations as probes for the structure of the galactic center

Symposium - International Astronomical Union ◽

10.1017/s0074180900084886 ◽

1998 ◽

Vol 184 ◽

pp. 271-272

Author(s):

K. Wada ◽

T. Minezaki ◽

K. Sakamoto ◽

H. Fukuda

Keyword(s):

Numerical Modeling ◽

Numerical Simulations ◽

Mass Distribution ◽

Galactic Center ◽

Dynamical Behavior ◽

Interstellar Gas ◽

Interstellar Gas In Galaxies ◽

Dynamical Parameters ◽

Pattern Speed ◽

Hydrodynamical Simulations

Numerical modeling of the interstellar gas in galaxies is an effective approach to infer galactic gravitational structure. This is because the dynamical behavior of gas is very sensitive to the background gravitational potential. Since the dynamical resonances depend closely on the mass distribution and the pattern speed of the non-axisymmetric component, it is possible to determine these dynamical parameters by comparison of numerical simulations and gas observations.

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A GLOBAL PERIOD-1 MOTION OF A PERIODICALLY EXCITED, PIECEWISE-LINEAR SYSTEM

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127405013071 ◽

2005 ◽

Vol 15 (06) ◽

pp. 1945-1957 ◽

Cited By ~ 19

Author(s):

SANTHOSH MENON ◽

ALBERT C. J. LUO

Keyword(s):

Linear System ◽

Numerical Simulations ◽

Piecewise Linear ◽

Dynamical Behavior ◽

Analytical Prediction ◽

Algebraic Equations ◽

Piecewise Linear System ◽

Nonlinear Algebraic Equations ◽

The Stability ◽

Nonsmooth Dynamical Systems

The period-1 motion of a piecewise-linear system under a periodic excitation is predicted analytically through the Poincaré mapping and the corresponding mapping sections formed by the switch planes pertaining to the two constraints. The mapping relationship generates a set of nonlinear algebraic equations from which the period-1 motion is determined analytically. The stability and bifurcation of the period-1 motion are determined, and numerical simulations are carried out for confirmation of the analytical prediction of period-1 motion. An unsymmetrical stable period-1 motion is observed. This investigation helps us understand the dynamical behavior of period-1 motion in the piecewise-linear system and more efficiently obtain other periodic motions and chaos through numerical simulations. The similar methodology presented in this paper can be used for other nonsmooth dynamical systems.

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Dynamics of a Predator-Prey Model with Fear Effect and Time Delay

Complexity ◽

10.1155/2021/9184193 ◽

2021 ◽

Vol 2021 ◽

pp. 1-16

Author(s):

Junli Liu ◽

Pan Lv ◽

Bairu Liu ◽

Tailei Zhang

Keyword(s):

Numerical Simulations ◽

Dynamical Behavior ◽

Normal Form Theory ◽

Predator Prey ◽

Center Manifold Theorem ◽

Predator Prey Model ◽

Prey Model ◽

Delay Dependent ◽

The Impact ◽

Dependent Factor

In this paper, we propose a time-delayed predator-prey model with Holling-type II functional response, which incorporates the gestation period and the cost of fear into prey reproduction. The dynamical behavior of this system is both analytically and numerically investigated from the viewpoint of stability, permanence, and bifurcation. We found that there are stability switches, and Hopf bifurcations occur when the delay τ passes through a sequence of critical values. The explicit formulae which determine the direction, stability, and other properties of the bifurcating periodic solutions are given by using the normal form theory and center manifold theorem. We perform extensive numerical simulations to explore the impact of some important parameters on the dynamics of the system. Numerical simulations show that high levels of fear have a stabilizing effect while relatively low levels of fear have a destabilizing effect on the predator-prey interactions which lead to limit-cycle oscillations. We also found that the model with or without a delay-dependent factor can have a significantly different dynamics. Thus, ignoring the delay or not including the delay-dependent factor might result in inaccurate modelling predictions.

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A Prey-Predator Model with Michael Mentence Type of Predator Harvesting and Infectious Disease in Prey

Iraqi Journal of Science ◽

10.24996/ijs.2020.61.5.23 ◽

2020 ◽

pp. 1146-1163

Author(s):

Hiba Abdullah Ibrahim ◽

Raid Kamel Naji

Keyword(s):

Infectious Disease ◽

Numerical Simulations ◽

Equilibrium Points ◽

Dynamical Behavior ◽

Local Bifurcation ◽

Persistence Conditions ◽

Analytical Results ◽

Predator Model ◽

Disease In Prey

A prey-predator model with Michael Mentence type of predator harvesting and infectious disease in prey is studied. The existence, uniqueness and boundedness of the solution of the model are investigated. The dynamical behavior of the system is studied locally as well as globally. The persistence conditions of the system are established. Local bifurcation near each of the equilibrium points is investigated. Finally, numerical simulations are given to show our obtained analytical results.

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Modeling and Simulation of Bifurcation Dynamics of a Double Spatial Pendulum Excited by a Rotating Obstacle

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455419501451 ◽

2019 ◽

Vol 19 (12) ◽

pp. 1950145

Author(s):

Grzegorz Kudra ◽

Michał Szewc ◽

Michał Ludwicki ◽

Jan Awrejcewicz

Keyword(s):

Modeling And Simulation ◽

Numerical Simulations ◽

Mechanical System ◽

Circular Plate ◽

Friction Force ◽

Contact Area ◽

Special Class ◽

Dynamical Behavior ◽

Finite Size ◽

Rotating Obstacle

This work focuses on analyzing the dynamical behavior of a mechanical system consisting of a double spatial pendulum in contact with a movable obstacle. The pendulum’s ability to move in space is achieved by the use of special Cardan–Hook joints as the links of the pendulum. The mechanical system is equipped with a special movable obstacle, i.e. a rotating circular plate situated below the pendulum, which limits the space of admissible positions. A significant part of this work is devoted to the modeling of the contact between the pendulum and the obstacle. In this regard, a special class of reduced models is derived with the resultant friction force and moment acting on the finite size of the contact area along with a compliant model of impact based on the Hertz stiffness. Finally, the effective model suitable for fast and realistic numerical simulations is obtained. The contact model is tested numerically and the effect of its parameters on the system bifurcation dynamics is investigated.

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Dynamical Behavior of a Stochastic SIRC Model for Influenza A

Symmetry ◽

10.3390/sym12050745 ◽

2020 ◽

Vol 12 (5) ◽

pp. 745 ◽

Cited By ~ 1

Author(s):

Tongqian Zhang ◽

Tingting Ding ◽

Ning Gao ◽

Yi Song

Keyword(s):

Lyapunov Function ◽

Numerical Simulations ◽

Positive Solution ◽

Epidemic Model ◽

Influenza A ◽

Dynamical Behavior ◽

Sufficient Conditions ◽

Global Positive Solution ◽

Theoretical Results ◽

Stochastic Lyapunov Function

In this paper, a stochastic SIRC epidemic model for Influenza A is proposed and investigated. First, we prove that the system exists a unique global positive solution. Second, the extinction of the disease is explored and the sufficient conditions for extinction of the disease are derived. And then the existence of a unique ergodic stationary distribution of the positive solutions for the system is discussed by constructing stochastic Lyapunov function. Furthermore, numerical simulations are employed to illustrate the theoretical results. Finally, we give some further discussions about the system.

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DYNAMICS OF A DELAYED EPIDEMIOLOGICAL MODEL WITH NONLINEAR INCIDENCE: THE ROLE OF INFECTED INCIDENCE FRACTION

Journal of Biological System ◽

10.1142/s0218339005001562 ◽

2005 ◽

Vol 13 (04) ◽

pp. 341-361 ◽

Cited By ~ 7

Author(s):

B. MUKHOPADHYAY ◽

R. BHATTACHARYYA

Keyword(s):

Numerical Simulations ◽

Incidence Rate ◽

Recovery Time ◽

Dynamical Behavior ◽

Vital Role ◽

Point Of View ◽

Epidemiological Model ◽

Discrete Form ◽

Fraction I

We present and analyze an epidemiological model containing Susceptible (S(t)) and Infected (I(t)) populations. The incidence rate is assumed to be nonlinear in the infected fraction (Ip(t)) as well as the susceptible fraction (Sq(t)). The dynamical behavior of the system is investigated from the point of view of stability and bifurcation. To model the recovery time of infected populations, a recovery delay, both in distributed and discrete form is introduced. In all the cases, it is shown that the infected incidence fraction p plays a vital role in controlling the dynamical behavior of the system. Numerical simulations are performed to justify the analytical findings.

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