Periodicity and bifurcation of a bouncing ball system with rigidly connected harmonic limiters

2020 ◽  
pp. 2150066
Author(s):  
Ruihai Li ◽  
Ruiyang Qiu
Keyword(s):  
Numerical Simulation ◽  
Local Stability ◽  
Relative Velocity ◽  
Sufficient Conditions ◽  
Restitution Coefficient ◽  
Bifurcation Diagrams ◽  
Bouncing Ball ◽  
Periodic Movement ◽  
Different Types ◽  
Simulation Results

The bouncing ball system with two rigidly connected harmonic limiters is revisited in order to further analyze its periodic movement and bifurcation dynamics. By using the impulsive impact maps, we obtain several sufficient conditions for the existence and local stability of three different types of periodic orbits, respectively, and then plot the bifurcation diagrams in the space of the relative velocity and the restitution coefficient for different parameters of the limiter. The numerical simulation results are consistent with those of the theoretical analysis.

scholarly journals Parameter Estimation and Hybrid Lag Synchronization in Hyperchaotic Lü Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Qing Wei ◽  
Zuolei Wang
Keyword(s):  
Numerical Simulation ◽  
Parameter Estimation ◽  
Adaptive Control ◽  
Lyapunov Stability ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Unknown Parameters ◽  
Lag Synchronization ◽  
Control Approach ◽  
Simulation Results

The antiphase and complete lag synchronization of hyperchaotic Lü systems with unknown parameters is investigated. Based on the Lyapunov stability theory, the sufficient conditions for achieving hybrid lag synchronization are derived. The optimized parameter observers are approached analytically via adaptive control approach. Numerical simulation results are presented to verify the effectiveness of the proposed scheme.

A CLASS OF INTERACTING PARTICLE SYSTEMS ON THE INFINITE CYLINDER WITH FLOCKING PHENOMENA

2012 ◽  
Vol 22 (07) ◽  
pp. 1250008 ◽  
Author(s):  
SEUNG-YEAL HA ◽  
MOON-JIN KANG ◽  
CORRADO LATTANZIO ◽  
BRUNO RUBINO
Keyword(s):  
Numerical Simulation ◽  
Interacting Particle Systems ◽  
Sufficient Conditions ◽  
Particle Systems ◽  
Kuramoto Model ◽  
Infinite Cylinder ◽  
Interacting Particle ◽  
Proposed Model ◽  
Simulation Results ◽  
Flocking Motion

We present a class of extended Kuramoto models describing a flocking motion of particles on the infinite cylinder and provide sufficient conditions for the asymptotic formation of locked solutions where the distance between particles remains constant. Our proposed model includes the complex Kuramoto model for synchronization. We also provide several numerical simulation results and compare them with analytical results.

FUNCTION PROJECTIVE SYNCHRONIZATION OF CHAOTIC SYSTEMS VIA NONLINEAR ADAPTIVE–IMPULSIVE CONTROL

2011 ◽  
Vol 22 (11) ◽  
pp. 1281-1291 ◽  
Author(s):  
RANCHAO WU ◽  
DONGXU CAO
Keyword(s):  
Numerical Simulation ◽  
Dynamical Systems ◽  
Chaotic Systems ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Projective Synchronization ◽  
Function Projective Synchronization ◽  
Simulation Results ◽  
Invariant Principle

In this paper, function projective synchronization of chaotic systems is investigated through nonlinear adaptive–impulsive control. To achieve synchronization, suitable nonlinear continuous and impulsive controllers are designed, according to invariant principle of impulsive dynamical systems. Sufficient conditions are given to ensure the synchronization. Numerical simulation results show the effectiveness of the proposed scheme.

Hopf Bifurcation and Hidden Attractors of a Delay-Coupled Duffing Oscillator

2015 ◽  
Vol 25 (12) ◽  
pp. 1550162 ◽  
Author(s):  
Huitao Zhao ◽  
Yiping Lin ◽  
Yunxian Dai
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Stable Equilibrium ◽  
Duffing Oscillator ◽  
Sufficient Conditions ◽  
Hidden Attractors ◽  
Characteristic Roots ◽  
Delayed System ◽  
Simulation Results ◽  
Spatio Temporal

In this paper, a delay-coupled Duffing equation is studied. By the characteristic roots technique, sufficient conditions are obtained for Hopf bifurcation occurrence. And the spatio-temporal patterns of the bifurcating periodic solutions are also obtained, some examples are given to demonstrate the theoretical analysis. Especially, the obtained numerical simulation results show that there are hidden attractors in this delayed system, which can coexist with stable equilibrium or stable bifurcating orbits.

scholarly journals Dynamic Analysis of the Symbiotic Model of Commensalism and Parasitism with Harvesting in Commensal Populations

2021 ◽  
Vol 5 (1) ◽  
pp. 193
Author(s):  
Nurmaini Puspitasari ◽  
Wuryansari Muharini Kusumawinahyu ◽  
Trisilowati Trisilowati
Keyword(s):  
Numerical Simulation ◽  
Dynamic Analysis ◽  
Local Stability ◽  
Equilibrium Points ◽  
Parasite Population ◽  
Asymptotically Stable ◽  
Population Extinction ◽  
Simulation Results ◽  
Extinction Point

This article discussed about a dynamic analysis of the symbiotic model of commensalism and parasitism with harvesting in the commensal population. This model is obtained from a modification of the symbiosis commensalism model. This modification is by adding a new population, namely the parasite population. Furthermore, it will be investigated that the three populations can coexist. The analysis carried out includes the determination of all equilibrium points along with their existence and local stability along with their stability requirements. From this model, it is obtained eight equilibrium points, namely three population extinction points, two population extinction points, one population extinction point and three extinction points can coexist. Of the eight points, only two points are asymptotically stable if they meet certain conditions. Next, a numerical simulation will be performed to illustrate the model’s behavior. In this article, a numerical simulation was carried out using the RK-4 method. The simulation results obtained support the results of the dynamic analysis that has been done previously.This article discussed about a dynamic analysis of the symbiotic model of The dynamics of the symbiotic model of commensalism and parasitism with harvesting in the commensal population. is the main focus of this study. This model is obtained from a modification of the symbiosis commensalism model. This modification is by adding a new population, namely the parasite population. Furthermore, it will be investigated that the three populations can coexist. The analysis carried out includes the determination begins by identifying the conditions for the existence of all equilibrium points along with their existence and local stability along with their stability requirements. From this model, it is obtained eight equilibrium points, namely three population extinction points, two population extinction points, one population extinction point and three extinction points can coexist. Of the eight points, only two points are asymptotically stable if they meet certain conditions. Next, a numerical simulation will be performed to illustrate the model’s behavior. In this article, a numerical simulation was carried out using the RK-4 method. The simulation results obtained support the results of the dynamic analysis that has been done previously.[VM1]  [VM1]To add a mathematical effect to the article. There can be added mathematical models produced in the study at the end of this section.

Development of a rotation-based negative stiffness device for seismic protection of structures

2016 ◽  
Vol 23 (5) ◽  
pp. 853-867 ◽  
Author(s):  
Navid Attary ◽  
M Symans ◽  
S Nagarajaiah
Keyword(s):  
Numerical Simulation ◽  
Conceptual Development ◽  
Power Source ◽  
Negative Stiffness ◽  
Analytical Models ◽  
Seismic Protection ◽  
Different Types ◽  
Negative Stiffness Device ◽  
Control Devices ◽  
Simulation Results

Researchers worldwide have developed various semi-active control devices for seismic protection of structures. Most of these devices are electromechanical in nature and thus require a power source for their operation. In this paper, a newly developed rotation-based mechanical adaptive passive device is presented. These unique devices are able to mechanically change stiffness, either by adding positive or negative stiffness, by using different types of rotational elements. The devices are compact due to their use of rotational elements, facilitating their implementation in structures. The conceptual development of these devices is presented herein along with analytical models and numerical simulation results that demonstrate their potential for providing seismic protection. In addition, an extension of the stiffness modulation concept is introduced wherein damping is modulated.

scholarly journals PEMODELAN MATEMATIKA TERHADAP PENYEBARAN VIRUS KOMPUTER DENGAN PROBABILITAS KEKEBALAN

2021 ◽  
Vol 3 (2) ◽  
pp. 122-132
Author(s):  
Neni Nur Laili Ersela Zain ◽  
Pardomuan Robinson Sihombing
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Basic Reproduction Number ◽  
Local Stability ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Minimum Size ◽  
Computer Viruses ◽  
Simulation Results ◽  
The Basic Reproduction Number

The increase in the number of computer viruses can be modeled with a mathematical model of the spread of SEIR type of diseases with immunity probability. This study aims to model the pattern of the spread of computer viruses. The method used in this research is the analytical method with the probability of mathematical immunity. Based on the analysis of the model, two equilibrium points free from disease E1 and endemic equilibrium points E2 were obtained. The existence and local stability of the equilibrium point depends on the basic reproduction number R0. Equilibrium points E1 and E2 tend to be locally stable because R0<1 which means there is no spread of disease. While the numerical simulation results shown that the size of the probability of immunity will affect compartment R and the minimum size of a new computer and the spread of computer viruses will affect compartments S and E on the graph of the simulation results. The conclusion obtained by the immune model SEIR successfully shows that increasing the probability of immunity significantly affects the increase in the number of computer hygiene after being exposed to a virus.

Determination of Loading Path for Warm Tube Hydroforming of Diamond Shaped Parts

2011 ◽  
Author(s):  
Wei Chen ◽  
L. C. Chan ◽  
T. C. Lee
Keyword(s):  
Numerical Simulation ◽  
Tube Hydroforming ◽  
Fem Simulation ◽  
Loading Path ◽  
Loading Paths ◽  
Different Types ◽  
Series Of Experiments ◽  
Simulation Results ◽  
Good Agreement

This paper aims to present an optimization process for three different types of loading paths studied in the numerical simulation of tube hydroforming of diamond-shaped sheet products. These three different types of loading paths werestudied in a numerical simulation of tube hydroforming of diamond-shaped products. The loading paths by which the best final shapes were obtained in the simulation were adopted in actual processing operation. A series of experiments were conducted within the temperature range of 270±10°C. Constitutive behavior was assumed to be elasto-plastic, and the material parameters used in the simulation were obtained from corresponding literature. The designed loading ratios were incorporated into the model to obtain the corresponding hydroforming results. The simulation results are used in the experimental verification and the products were compared with the simulation results. The experimental results showed a good agreement with the predicted numerical results, indicating that FEM simulation is an effective tool in optimizing processing procedures.

Synchronizing the Noise-Perturbed Rössler Hyperchaotic System via Sliding Mode Control

2011 ◽  
Vol 66 (1-2) ◽  
pp. 6-12 ◽  
Author(s):  
Jianwen Feng ◽  
Phillip Yam ◽  
Francis Austin ◽  
Chen Xu
Keyword(s):  
Numerical Simulation ◽  
Sliding Mode Control ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Hyperchaotic System ◽  
Mode Control ◽  
Synchronization Problem ◽  
Control Concept ◽  
Simulation Results ◽  
Hyperchaotic Systems

This paper investigates the synchronization problem between two unidirectionally-coupled Rössler hyperchaotic systems in the presence of noise perturbations. Sufficient conditions are obtained for synchronization by using a particularly simple linear sliding mode surface that is based on the sliding mode control concept. Only one controller function is needed to achieve synchronization in our present approach which makes it much easier to implement in contrast to many other synchronization schemes that require two or more controllers. Numerical simulation results are also included to illustrate the superior features of this new scheme.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj&gt; 0 for eachj&gt; 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

Sign in / Sign up

Export Citation Format

Share Document