Chaotic Dynamics of Piezoelectric Composite Laminated Beams

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Liangqiang Zhou ◽  
Wen Wang
Keyword(s):  
Numerical Simulations ◽  
Chaotic Motion ◽  
Pulse Sequence ◽  
Homoclinic Orbits ◽  
Dissipation Factor ◽  
Piezoelectric Composite ◽  
Phase Method ◽  
Global Dynamics ◽  
Laminated Beams ◽  
Normal Form Theory

Chaos in piezoelectric composite laminated beams has significant implications in the design of this model. Some results for this model have been obtained numerically. With the energy-phase method and numerical simulations, global dynamics of piezoelectric composite laminated beams is investigated in this paper. The average equation of the piezoelectric composite laminated beam is obtained by the normal form theory. The existence of multipulse homoclinic orbits for undisturbed and dissipative cases is analyzed by the energy-phase method, and the mechanism of chaotic motion of the system is given. The effect of the dissipation factor on pulse sequence and layer radius is studied in detail. The chaotic motion of the system is verified by numerical simulations.

scholarly journals Multipulse Homoclinic Orbits and Chaotic Dynamics of a Reinforced Composite Plate with Carbon Nanotubes

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Fengxian An ◽  
Fangqi Chen ◽  
Xiaoxia Bian ◽  
Li Zhang
Keyword(s):  
Carbon Nanotubes ◽  
Normal Form ◽  
Composite Plate ◽  
Chaotic Dynamics ◽  
Homoclinic Orbits ◽  
Phase Method ◽  
Chaotic Motions ◽  
Normal Form Theory ◽  
Reinforced Composite ◽  
Averaged Equations

The multipulse homoclinic orbits and chaotic dynamics of a reinforced composite plate with the carbon nanotubes (CNTs) under combined in-plane and transverse excitations are studied in the case of 1 : 1 internal resonance. The method of multiple scales is adopted to derive the averaged equations. From the averaged equations, the normal form theory is applied to reduce the equations to a simpler normal form associated with a double zero and a pair of pure imaginary eigenvalues. The energy-phase method proposed by Haller and Wiggins is utilized to examine the global bifurcations and chaotic dynamics of the CNT-reinforced composite plate. The analytical results demonstrate that the multipulse Shilnikov-type homoclinic orbits and chaotic motions exist in the system. Homoclinic trees are constructed to illustrate the repeated bifurcations of multipulse solutions. In order to verify the theoretical results, numerical simulations are given to show the multipulse Shilnikov-type chaotic motions in the CNT-reinforced composite plate. The results obtained here imply that the motion is chaotic in the sense of the Smale horseshoes for the CNT-reinforced composite plate.

Dynamics analysis of a gyrostat system with intermittent forcing

2021 ◽  
pp. 095965182110590
Author(s):  
Jianbin He ◽  
Jianping Cai
Keyword(s):  
Lyapunov Exponent ◽  
Numerical Simulations ◽  
Periodic Motion ◽  
Chaotic Motion ◽  
Dynamics Analysis ◽  
Bifurcation Diagrams ◽  
Stable Point ◽  
Dynamical Characteristics ◽  
Main Work ◽  
Selection Of

The dynamical characteristics of a gyrostat system with intermittent forcing are investigated, the main work and contributions are given as follows: (1) The gyrostat system with an intermittent forcing is studied, and its dynamical characteristics are investigated by the corresponding Lyapunov exponent spectrums and bifurcation diagrams with respect to the amplitude of intermittent forcing. The modified gyrostat system exists chaotic motion when the amplitude of intermittent forcing belongs to a certain interval, and it can be at a state of stable point or periodic motion by the design of amplitude. (2) The gyrostat system with multiple intermittent forcings is also investigated through the combination of Lyapunov exponent spectrums and bifurcation diagrams, and it behaves periodic motion or chaotic motion when the amplitude or forcing width is different. (3) By the selection of parameters in intermittent forcings, the modified gyrostat system is at a state of stable point, periodic motion or chaotic motion. Numerical simulations verify the feasibility and effectiveness of the modified gyrostat system.

scholarly journals Stability, Bifurcation, and Quenching Chaos of a Vehicle Suspension System

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Chun-Cheng Chen ◽  
Shun-Chang Chang
Keyword(s):  
Chaotic Motion ◽  
Control Method ◽  
Homoclinic Orbits ◽  
Suspension System ◽  
State Feedback Control ◽  
Phase Portraits ◽  
Frequency Spectra ◽  
The Road ◽  
Dynamics And Control ◽  
Vehicle Suspension System

This study investigated the dynamics and control of a nonlinear suspension system using a quarter-car model that is forced by the road profile. Bifurcation analysis used to characterize nonlinear dynamic behavior revealed codimension-two bifurcation and homoclinic orbits. The nonlinear dynamics were determined using bifurcation diagrams, phase portraits, Poincaré maps, frequency spectra, and Lyapunov exponents. The Lyapunov exponent was used to identify the onset of chaotic motion. Finally, state feedback control was used to prevent chaotic motion. The effectiveness of the proposed control method was determined via numerical simulations.

Dynamic Analysis of an SIRS Model with Nonlinear Incidence Rate

2012 ◽  
Vol 155-156 ◽  
pp. 23-26
Author(s):  
Jun Hong Li ◽  
Ning Cui ◽  
Liang Cui ◽  
Cai Juan Li
Keyword(s):  
Hopf Bifurcation ◽  
Dynamic Analysis ◽  
Numerical Simulations ◽  
Epidemic Model ◽  
Global Dynamics ◽  
Nonlinear Incidence Rate ◽  
Dulac Function ◽  
Sirs Epidemic Model ◽  
Sirs Model ◽  
Disease Free

In this paper, we study the global dynamics of an SIRS epidemic model with nonlinear inci- dence rate. By means of Dulac function and Poincare-Bendixson Theorem, we proved the global asy- mptotical stable results of the disease-free equilibrium. It is then obtained the model undergoes Hopf bifurcation and existence of one limit cycle. Some numerical simulations are given to illustrate the an- alytical results.

scholarly journals Global Dynamics of a Mathematical Model on Smoking

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Zainab Alkhudhari ◽  
Sarah Al-Sheikh ◽  
Salma Al-Tuwairqi
Keyword(s):  
Mathematical Model ◽  
Global Stability ◽  
Numerical Simulations ◽  
The Other ◽  
Global Dynamics ◽  
Local And Global Stability ◽  
Two Equilibria

We derive and analyze a mathematical model of smoking in which the population is divided into four classes: potential smokers, smokers, temporary quitters, and permanent quitters. In this model we study the effect of smokers on temporary quitters. Two equilibria of the model are found: one of them is the smoking-free equilibrium and the other corresponds to the presence of smoking. We examine the local and global stability of both equilibria and we support our results by using numerical simulations.

EXCITATORY–INHIBITORY NETWORKS WITH DYNAMICAL THRESHOLDS

1990 ◽  
Vol 01 (03) ◽  
pp. 249-257 ◽  
Author(s):  
D. Horn ◽  
M. Usher
Keyword(s):  
Differential Equations ◽  
Numerical Simulations ◽  
Chaotic Motion ◽  
Inhibitory Neurons ◽  
Network Configuration ◽  
Dynamic Features ◽  
Mixed States ◽  
Dynamical Parameters ◽  
Feedback Networks ◽  
Inhibitory Networks

We investigate feedback networks containing excitatory and inhibitory neurons. The couplings between the neurons follow a Hebbian rule in which the memory patterns are encoded as cell assemblies of the excitatory neurons. Using disjoint patterns, we study the attractors of this model and point out the importance of mixed states. The latter become dominant at temperatures above 0.25. We use both numerical simulations and an analytic approach for our investigation. The latter is based on differential equations for the activity of the different memory patterns in the network configuration. Allowing the excitatory thresholds to develop dynamic features which correspond to fatigue of individual neurons, we obtain motion in pattern space, the space of all memories. The attractors turn into transients leading to chaotic motion for appropriate values of the dynamical parameters. The motion can be guided by overlaps between patterns, resembling a process of free associative thinking in the absence of any input.

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

Complexity ◽  
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.

scholarly journals Heteronuclear and homonuclear radio-frequency-driven recoupling

2021 ◽  
Vol 2 (1) ◽  
pp. 343-353
Author(s):  
Evgeny Nimerovsky ◽  
Kai Xue ◽  
Kumar Tekwani Movellan ◽  
Loren B. Andreas
Keyword(s):  
Radio Frequency ◽  
Numerical Simulations ◽  
Crucial Role ◽  
Pulse Sequence ◽  
Magic Angle Spinning ◽  
Magic Angle ◽  
Dipolar Interactions ◽  
Phase Cycling ◽  
Angle Spinning

Abstract. The radio-frequency-driven recoupling (RFDR) pulse sequence is used in magic-angle spinning (MAS) NMR to recouple homonuclear dipolar interactions. Here we show simultaneous recoupling of both the heteronuclear and homonuclear dipolar interactions by applying RFDR pulses on two channels. We demonstrate the method, called HETeronuclear RFDR (HET-RFDR), on microcrystalline SH3 samples at 10 and 55.555 kHz MAS. Numerical simulations of both HET-RFDR and standard RFDR sequences allow for better understanding of the influence of offsets and paths of magnetization transfers for both HET-RFDR and RFDR experiments, as well as the crucial role of XY phase cycling.

scholarly journals Global dynamics and spatio-temporal patterns of predator–prey systems with density-dependent motion

2020 ◽  
pp. 1-31
Author(s):  
HAI-YANG JIN ◽  
ZHI-AN WANG
Keyword(s):  
Pattern Formation ◽  
Numerical Simulations ◽  
Prey Density ◽  
Temporal Patterns ◽  
Steady States ◽  
Global Dynamics ◽  
Predator Prey ◽  
Density Dependent ◽  
Spatially Homogeneous ◽  
Spatio Temporal

In this paper, we investigate the global boundedness, asymptotic stability and pattern formation of predator–prey systems with density-dependent prey-taxis in a two-dimensional bounded domain with Neumann boundary conditions, where the coefficients of motility (diffusiq‘dfdon) and mobility (prey-taxis) of the predator are correlated through a prey density-dependent motility function. We establish the existence of classical solutions with uniform-in time bound and the global stability of the spatially homogeneous prey-only steady states and coexistence steady states under certain conditions on parameters by constructing Lyapunov functionals. With numerical simulations, we further demonstrate that spatially homogeneous time-periodic patterns, stationary spatially inhomogeneous patterns and chaotic spatio-temporal patterns are all possible for the parameters outside the stability regime. We also find from numerical simulations that the temporal dynamics between linearised system and nonlinear systems are quite different, and the prey density-dependent motility function can trigger the pattern formation.

Dynamics of SVEIS epidemic model with distinct incidence

2015 ◽  
Vol 08 (06) ◽  
pp. 1550076 ◽  
Author(s):  
N. Nyamoradi ◽  
M. Javidi ◽  
B. Ahmad
Keyword(s):  
Numerical Simulations ◽  
Dynamic Behavior ◽  
Epidemic Model ◽  
Stability Theory ◽  
Global Dynamics ◽  
Turing Bifurcation ◽  
Diffusive Model ◽  
Stability And Bifurcation ◽  
Matrix Stability ◽  
Bifurcation Behavior

In this paper, we study the global dynamics of a SVEIS epidemic model with distinct incidence for exposed and infectives. The model is analyzed for stability and bifurcation behavior. To account for the realistic phenomenon of non-homogeneous mixing, the effect of diffusion on different population subclasses is considered. The diffusive model is analyzed using matrix stability theory and conditions for Turing bifurcation are derived. Numerical simulations support our analytical results on the dynamic behavior of the model.

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