Insight Into the Drift Motion of a Bouncing Asymmetric Dimer

2019 ◽  
Vol 14 (6) ◽  
Author(s):  
Runsen Zhang ◽  
Zhen Zhao ◽  
Xudong Zheng ◽  
Qi Wang
Keyword(s):  
Numerical Simulations ◽  
Opposite Direction ◽  
Drift Motion ◽  
System Parameters ◽  
Asymmetric Dimer ◽  
Double Impact ◽  
Theoretical Results ◽  
Drift Direction ◽  
Insight Into ◽  
Vibrating Plate

The drift motion of an asymmetric dimer bouncing on a harmonically vibrating plate is addressed in this paper. The direction of this motion is determined by the behavior of the dimer during a double impact. Namely, if the system parameters allow a sticking impact as a generic behavior, the dimer drifts in one direction, whereas if all impacts end in a reverse slip, the dimer drifts in the opposite direction. By this mechanism, the bifurcation coefficients dominating the drift direction are obtained and discussed. But strictly speaking, the drift direction does not change unless the reverse slipping displacement after a double impact is big enough. Thus, numerical simulations are carried out to find a more accurate threshold and check the rationality of theoretical results.

Application of Double Impact Oscillator in Forming

2001 ◽  
Author(s):  
František Peterka
Keyword(s):  
Numerical Simulations ◽  
Single System ◽  
Impact Oscillator ◽  
System Parameters ◽  
Impact Oscillators ◽  
Simulation Results ◽  
The Impact ◽  
Impact Motion ◽  
Double Impact ◽  
Phase Motion

Abstract The double impact oscillator represents two symmetrically arranged single impact oscillators. It is the model of a forming machine, which does not spread the impact impulses into its neighborhood. The anti-phase impact motion of this system has the identical dynamics as the single system. The in-phase motion and the influence of asymmetries of the system parameters are studied using numerical simulations. Theoretical and simulation results are verified experimentally.

On the kinetics of Hadamard-type fractional differential systems

2020 ◽  
Vol 23 (2) ◽  
pp. 553-570 ◽  
Author(s):  
Li Ma
Keyword(s):  
Differential Operator ◽  
Numerical Simulations ◽  
Type Inequality ◽  
The Other ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Kinetics Of ◽  
Theoretical Results

AbstractThis paper is devoted to the investigation of the kinetics of Hadamard-type fractional differential systems (HTFDSs) in two aspects. On one hand, the nonexistence of non-trivial periodic solutions for general HTFDSs, which are considered in some functional spaces, is proved and the corresponding eigenfunction of Hadamard-type fractional differential operator is also discussed. On the other hand, by the generalized Gronwall-type inequality, we estimate the bound of the Lyapunov exponents for HTFDSs. In addition, numerical simulations are addressed to verify the obtained theoretical results.

scholarly journals A Stochastic SIR Epidemic System with a Nonlinear Relapse

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Ali El Myr ◽  
Abdelaziz Assadouq ◽  
Lahcen Omari ◽  
Adel Settati ◽  
Aadil Lahrouz
Keyword(s):  
Numerical Simulations ◽  
Stationary Distribution ◽  
Stochastic Perturbations ◽  
Sir Epidemic ◽  
Spread Model ◽  
Stochastic Sir ◽  
Theoretical Results

We investigate the conditions that control the extinction and the existence of a unique stationary distribution of a nonlinear mathematical spread model with stochastic perturbations in a population of varying size with relapse. Numerical simulations are carried out to illustrate the theoretical results.

Global Analysis of the Double Impact Oscillator Dynamics

1999 ◽  
Author(s):  
František Peterka
Keyword(s):  
Global Analysis ◽  
Impact Oscillator ◽  
System Parameters ◽  
Impact Oscillators ◽  
Real Value ◽  
Simulation Results ◽  
The Impact ◽  
Impact Motion ◽  
Double Impact ◽  
Phase Motion

Abstract The double impact oscillator represents two symmetrically arranged single impact oscillators. It is the model of a forming machine, which does not spread the impact impulses into its neighbourhood. The anti-phase impact motion of this system has the identical dynamics as the single system. The in-phase motion and the influence of asymmetries of the system parameters are studied using numerical simulations. Theoretical and simulation results are verified experimentally and the real value of the restitution coefficient is determined by this method.

More Dynamical Properties Revealed from a 3D Lorenz-like System

2014 ◽  
Vol 24 (10) ◽  
pp. 1450133 ◽  
Author(s):  
Haijun Wang ◽  
Xianyi Li
Keyword(s):  
Numerical Simulations ◽  
Local Stability ◽  
Equilibrium Points ◽  
Heteroclinic Orbits ◽  
Mathematical Work ◽  
Chaotic Attractors ◽  
Heteroclinic Cycles ◽  
Homoclinic And Heteroclinic Orbits ◽  
Dynamical Properties ◽  
Theoretical Results

After a 3D Lorenz-like system has been revisited, more rich hidden dynamics that was not found previously is clearly revealed. Some more precise mathematical work, such as for the complete distribution and the local stability and bifurcation of its equilibrium points, the existence of singularly degenerate heteroclinic cycles as well as homoclinic and heteroclinic orbits, and the dynamics at infinity, is carried out in this paper. In particular, another possible new mechanism behind the creation of chaotic attractors is presented. Based on this mechanism, some different structure types of chaotic attractors are numerically found in the case of small b > 0. All theoretical results obtained are further illustrated by numerical simulations. What we formulate in this paper is to not only show those dynamical properties hiding in this system, but also (more mainly) present a kind of way and means — both "locally" and "globally" and both "finitely" and "infinitely" — to comprehensively explore a given system.

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

2012 ◽  
Vol 22 (04) ◽  
pp. 1250092 ◽  
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.

Dynamics of a stochastic three-species competitive model with Lévy jumps

2018 ◽  
Vol 11 (05) ◽  
pp. 1850075
Author(s):  
Yongxin Gao ◽  
Shiquan Tian
Keyword(s):  
Numerical Simulations ◽  
Critical Value ◽  
Persistence In The Mean ◽  
Competitive Model ◽  
Stability In Distribution ◽  
Parameters Analysis ◽  
The Mean ◽  
Lévy Jumps ◽  
White Noises ◽  
Theoretical Results

This paper is concerned with a three-species competitive model with both white noises and Lévy noises. We first carry out the almost complete parameters analysis for the model and establish the critical value between persistence in the mean and extinction for each species. The sufficient criteria for stability in distribution of solutions are obtained. Finally, numerical simulations are carried out to verify the theoretical results.

scholarly journals Stability of a Nonlinear Stochastic Epidemic Model with Transfer from Infectious to Susceptible

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Yanmei Wang ◽  
Guirong Liu
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Method ◽  
Deterministic Model ◽  
Vital Role ◽  
Nonlinear Incidence Rate ◽  
Sirs Model ◽  
Stochastic Epidemic ◽  
Almost Surely Exponential Stability ◽  
Theoretical Results ◽  
Disease Free

We investigate a stochastic SIRS model with transfer from infectious to susceptible and nonlinear incidence rate. First, using stochastic stability theory, we discuss stochastic asymptotic stability of disease-free equilibrium of this model. Moreover, if the transfer rate from infectious to susceptible is sufficiently large, disease goes extinct. Then, we obtain almost surely exponential stability of disease-free equilibrium, which implies that noises can lead to extinction of disease. By the Lyapunov method, we give conditions to ensure that the solution of this model fluctuates around endemic equilibrium of the corresponding deterministic model in average time. Furthermore, numerical simulations show that the fluctuation increases with increase in noise intensity. Finally, these theoretical results are verified by numerical simulations. Hence, noises play a vital role in epidemic transmission. Our results improve and extend previous related results.

scholarly journals Combination Difference Synchronization between Identical Generalised Lotka-Volterra Chaotic Systems

2020 ◽  
Vol 12 (2) ◽  
pp. 183-188 ◽  
Author(s):  
P. Trikha ◽  
Nasreen ◽  
L. S. Jahanzaib
Keyword(s):  
Numerical Simulations ◽  
Chaotic Systems ◽  
Complete Agreement ◽  
Theoretical Results ◽  
Combination Difference

This manuscript investigates the combination difference synchronization between identical Generalised Lotka-Volterra Chaotic Systems. Numerical Simulations have been performed which are in complete agreement of theoretical results.

scholarly journals Dynamics of a Prey–Predator System with Foraging Facilitation in Predators

2020 ◽  
Vol 30 (01) ◽  
pp. 2050009
Author(s):  
Yong Yao
Keyword(s):  
Numerical Simulations ◽  
Real Root ◽  
Qualitative Properties ◽  
Isolation Technique ◽  
Root Isolation ◽  
Number Of Equilibria ◽  
Complete Investigation ◽  
Theoretical Results ◽  
Predator System ◽  
Real Root Isolation

The dynamics of a prey–predator system with foraging facilitation among predators are investigated. The analysis involves the computation of many semi-algebraic systems of large degrees. We apply the pseudo-division reduction, real-root isolation technique and complete discrimination system of polynomial to obtain the parameter conditions for the exact number of equilibria and their qualitative properties as well as do a complete investigation of bifurcations including saddle-node, transcritical, pitchfork, Hopf and Bogdanov–Takens bifurcations. Moreover, numerical simulations are presented to support our theoretical results.

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