Nonlinear Dynamical Behavior in the Photodecomposition of N-Bromo-1,4-Benzoquinone-4-Imine

2013 ◽  
Vol 117 (22) ◽  
pp. 4545-4550 ◽  
Author(s):  
Jeffrey G. Bell ◽  
James R. Green ◽  
Jichang Wang
Keyword(s):  
Dynamical Behavior ◽  
Nonlinear Dynamical

scholarly journals Bistable dynamics beyond rotating wave approximation

2014 ◽  
Vol 23 (02) ◽  
pp. 1450019 ◽  
Author(s):  
Y. A. Sharaby ◽  
S. Lynch ◽  
A. Joshi ◽  
S. S. Hassan
Keyword(s):  
Ring Cavity ◽  
Dynamical Behavior ◽  
Single Mode ◽  
Unstable State ◽  
Nonlinear Dynamical ◽  
Rotating Wave Approximation ◽  
Wave Approximation ◽  
Atomic Medium ◽  
Bistable Dynamics ◽  
Rotating Wave

In this paper, we investigate the nonlinear dynamical behavior of dispersive optical bistability (OB) for a homogeneously broadened two-level atomic medium interacting with a single mode of the ring cavity without invoking the rotating wave approximation (RWA). The periodic oscillations (self-pulsing) and chaos of the unstable state of the OB curve is affected by the counter rotating terms through the appearance of spikes during its periods. Further, the bifurcation with atomic detuning, within and outside the RWA, shows that the OB system can be converted from a chaotic system to self-pulsing system and vice-versa.

Stable and Unstable Quasiperiodic Oscillations in Robot Dynamics

1993 ◽  
Author(s):  
G. Stépán ◽  
G. Haller
Keyword(s):  
Nonlinear Dynamical Systems ◽  
Dynamical Behavior ◽  
Time Lag ◽  
Nonlinear Behavior ◽  
Degree Of Freedom ◽  
Robot Dynamics ◽  
Robot Arm ◽  
Delayed Systems ◽  
Nonlinear Dynamical ◽  
Quasiperiodic Oscillations

Abstract Delays in robot control may result in unexpectedly sophisticated nonlinear dynamical behavior. Experiments on force controlled robots frequently show periodic and quasiperiodic oscillations which cannot be explained without including the time lag and/or the sampling time of the system in our models. Delayed systems, even of low degree of freedom, can produce phenomena which are already well understood in the theory of nonlinear dynamical systems but hardly ever occur in simple mechanical models. To illustrate this, we analyze the delayed positioning of a single degree of freedom robot arm. The analytical results show typical nonlinear behavior in the system which may go through a codimension two Hopf bifurcation for an infinite set of parameter values, leading to the creation of two-tori in the phase space. These results give a qualitative explanation for the existence of self-excited quasiperiodic oscillations in the dynamics of force controlled robots.

Generating Fully Bounded Chaotic Attractors

2013 ◽  
pp. 148-153
Author(s):  
Zeraoulia Elhadj
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Dynamical Behavior ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Nonlinear Dynamical ◽  
Dynamical Properties ◽  
The Given

Generating chaotic attractors from nonlinear dynamical systems is quite important because of their applicability in sciences and engineering. This paper considers a class of 2-D mappings displaying fully bounded chaotic attractors for all bifurcation parameters. It describes in detail the dynamical behavior of this map, along with some other dynamical phenomena. Also presented are some phase portraits and some dynamical properties of the given simple family of 2-D discrete mappings.

Is There a Relation Between Synchronization Stability and Bifurcation Type?

2020 ◽  
Vol 30 (08) ◽  
pp. 2050123
Author(s):  
Zahra Faghani ◽  
Zhen Wang ◽  
Fatemeh Parastesh ◽  
Sajad Jafari ◽  
Matjaž Perc
Keyword(s):  
Complex Networks ◽  
Nonlinear Dynamical Systems ◽  
General Relation ◽  
Dynamical Behavior ◽  
Stability Function ◽  
Nonlinear Dynamical ◽  
Practical Applications ◽  
Stability Functions ◽  
Stability And Bifurcation ◽  
The Stability

Synchronization in complex networks is an evergreen subject with many practical applications across the natural and social sciences. The stability of synchronization is thereby crucial for determining whether the dynamical behavior is stable or not. The master stability function is commonly used to that effect. In this paper, we study whether there is a relation between the stability of synchronization and the proximity to certain bifurcation types. We consider four different nonlinear dynamical systems, and we determine their master stability functions in dependence on key bifurcation parameters. We also calculate the corresponding bifurcation diagrams. By means of systematic comparisons, we show that, although there are some variations in the master stability functions in dependence on bifurcation proximity and type, there is in fact no general relation between synchronization stability and bifurcation type. This has important implication for the restrained generalizability of findings concerning synchronization in complex networks for one type of node dynamics to others.

scholarly journals A Review of Phase Space Topology Methods for Vibration-Based Fault Diagnostics in Nonlinear Systems

2019 ◽  
Vol 8 (3) ◽  
pp. 393-401 ◽  
Author(s):  
T. Haj Mohamad ◽  
Foad Nazari ◽  
C. Nataraj
Keyword(s):  
Phase Space ◽  
Nonlinear Systems ◽  
Dynamic Systems ◽  
Dynamical Behavior ◽  
Fault Diagnostics ◽  
Nonlinear Dynamical ◽  
Space Topology ◽  
Nonlinear Features ◽  
Phase Space Topology

Abstract Background In general, diagnostics can be defined as the procedure of mapping the information obtained in the measurement space to the presence and magnitude of faults in the fault space. These measurements, and especially their nonlinear features, have the potential to be exploited to detect changes in dynamics due to the faults. Purpose We have been developing some interesting techniques for fault diagnostics with gratifying results. Methods These techniques are fundamentally based on extracting appropriate features of nonlinear dynamical behavior of dynamic systems. In particular, this paper provides an overview of a technique we have developed called Phase Space Topology (PST), which has so far displayed remarkable effectiveness in unearthing faults in machinery. Applications to bearing, gear and crack diagnostics are briefly discussed.

scholarly journals Stability and Bifurcation Analysis of a Three-Dimensional Recurrent Neural Network with Time Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Yingguo Li
Keyword(s):  
Neural Network ◽  
Time Delay ◽  
Recurrent Neural Network ◽  
Center Manifold ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Nonlinear Dynamical ◽  
Bifurcation Direction ◽  
The Stability ◽  
Manifold Theory

We consider the nonlinear dynamical behavior of a three-dimensional recurrent neural network with time delay. By choosing the time delay as a bifurcation parameter, we prove that Hopf bifurcation occurs when the delay passes through a sequence of critical values. Applying the nor- mal form method and center manifold theory, we obtain some local bifurcation results and derive formulas for determining the bifurcation direction and the stability of the bifurcated periodic solution. Some numerical examples are also presented to verify the theoretical analysis.

scholarly journals Using passive control by a pendulum in a portal frame platform with piezoelectric energy harvesting

2017 ◽  
Vol 24 (16) ◽  
pp. 3684-3697 ◽  
Author(s):  
Rodrigo T Rocha ◽  
Jose M Balthazar ◽  
Angelo M Tusset ◽  
Vinicius Piccirillo
Keyword(s):  
Energy Harvesting ◽  
Periodic Orbit ◽  
Internal Resonance ◽  
Passive Control ◽  
Dynamical Behavior ◽  
Frame Structure ◽  
Nonlinear Dynamical ◽  
Piezoelectric Energy ◽  
Portal Frame ◽  
Portal Frame Structure

This work presents a passive control strategy using a pendulum on a simple portal frame structure, with two-to-one internal resonance, with a piezoelectric material coupling as a means of energy harvesting. In addition, the system is externally base-excited by an electro-dynamical shaker with harmonic output. Due to internal resonance the system may present the phenomenon of saturation, which provides some nonlinear dynamical behavior to the system. A pendulum is coupled to control nonlinear behaviors, leading to a periodic orbit, which is necessary to maintain energy harvesting. The results show that the system presents, most of the time, as being quasiperiodic. However, it does not present as being chaotic. With the pendulum, it was possible to control most of these quasiperiodic behaviors, leading to a periodic orbit. Moreover, it is possible to eliminate the need for an active or semi-active control, which are usually more complex. In addition, the control provides a way to detune the energy captured to the desired operating frequency.

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