Spectral, Entropy and Bifurcation Analysis of the Dynamics of a Catalyst Chemical Reverse-Flow Tubular Reactor

Oscillations, including chaotic ones, can spontaneously appear in chemical reactors or lean premixed combustors. Such behavior of the system is undesirable and should be identified at the stage of its modeling. This article analyzes the behavior of reverse-flow tubular chemical reactor with longitudinal dispersion in terms of chaotic oscillations. The purpose of using reverse flow is to increase the conversion degree. For the analysis of the reactor, among others, spectral analysis, entropy, and bifurcation analysis were used. The obtained results show the chaotic behavior of the reactor in a wide range of changes in the parameter’s values.

The State-space Model of Micro-chaos

Micro-chaos is the phenomenon when the sampling, the delay and the round-off lead to small amplitude chaotic oscillations in a digitally controlled system. It has been proved mathematically during the last few years in a couple of simple cases that the evolving vibrations are indeed chaotic. In this study, we partially generalize these results to the case when an originally unstable state of a system is stabilized by digital feedback control. It is pointed out that this type of systems are sensitive to initial conditions and there exists a finite attracting domain in their phase-space. We also show that the oscillations, related to micro-chaos may have a considerable influence on the accuracy and settling time of the control system. The application of numerical techniques is unavoidable in the case of chaotic systems. Several possibilities are highlighted in the paper for the numerical determination of important characteristics of microchaotic oscillations.

The Methodology of Distinguish Between Random and Chaotic Machine Tool Oscillations

Machine tool oscillations are irregular or aperiodic. Most often, these oscillations are chaotic but, in some cases, they can be quasi-periodic or random. The methodology for characterizing oscillations in the first of two steps uses the nonparametric hypothesis tests which the observed oscillations confirmed as irregular. The methodology for the final characterization of oscillations is based on chaos quantifiers. A time series defined as the measured values of oscillations in the time domain is the basis for calculating the quantifiers of chaos. There are four quantifiers of chaos: the Lyapunov exponent, Kolmogorov entropy, fractal dimension and correlation dimension. The correlation dimension and Kolmogorov entropy are important for distinguishing between random and chaotic oscillations. Other quantifiers of chaos are not used for this purpose. The methodology requires a multidisciplinary approach based on combining Nonlinear Dynamics and Probability Theory and Statistics. The methodology can be applied to many oscillating phenomena. Therefore, the paper mainly used the term oscillations, not vibrations, chatter, etc.

Nonlinear Dynamics of Cross-Flow Tubes Subjected to Initial Axial Load and Distributed Impacting Constraints

The dynamics of cross-flow tubes were studied in consideration of initial axial load and distributed impacting constraints, modeled as cubic and trilinear spring constraints. The tubes were modeled as Euler–Bernoulli beams and supported at both ends, including the simply supported tube and clamped-clamped tube. The analytical model involves a time-delayed displacement term induced by the cross flow based on the quasi-steady theory. For simplicity, a single flexible supported beam in a rigid square array of cylinders was studied by using the damping-controlled mechanism. The mean extension of the tube was considered, and thus, it added another nonlinear term in the equation of motion. Results show that the tube loses stability by buckling and fluttering at various initial pressure loads and cross-flow velocities. An increase was observed for critical velocities and initial pressure loads. Chaotic oscillations were observed for the trilinear spring model. The distribution of the impacting forces was also calculated. Some of the fresh results obtained in the impact system are expected to be helpful in understanding and controlling the dynamic responses of fluid-conveying pipes.

Entrainment of Chaotic Oscillations in a Colonial Tunicate.

BackgroundTunicates comprise an invertebrate, chordate subphylum which has been shown to be the closest group to vertebrates. Colonial tunicates are clusters of genetic clones generated asexually from a single free swimming larval “tadpole”. Each individual, or zooid, of the colony has a peristaltic heart which circulates blood through that individual. In addition, each zooid is connected to a common, external vascular network. This vascular network has radial extensions that end at the colony periphery in bulbs, or ampullae, which contract and expand to generate reciprocating flow between ampullae and zooids. Surgically detached ampullae continue to beat.ResultsQuantitative scans of videos of individual ampullae in a young Botrylloides viocella colony demonstrate ampullae contractions are often in phase, with occasional abrupt phase shifts out of and back to synchrony. The vessels connecting the ampullae to the zooid also contract, mostly in phase with the ampullae. Total volumes pumped by this colonial system are a significant fraction of the zooid volume, since it contracts 180 degrees out of phase and at the same frequency as the ampullae. Reversals of the peristaltic heart are at least partially synchronized with ampullae contractions. Ampullae that have been surgically detached from the colony contract at a more uniform rate with more symmetrical profiles than when part of the colony. ConclusionContractions of the ampullae and associated vessels pump sufficient blood in and out of the zooid that they should be considered functional hearts, and the partial synchrony of ampullae contractions results in a larger blood flow compared to an alternative asynchronous contraction pattern. The manner in which the ampullae abruptly fall out of and back to synchrony indicates synchrony is due to entrainment while the out of phase contractions of the zooid may be a direct result of pumping. The shape of contraction curves of detached ampullae pairs is almost indistinguishable from a pure sine wave, indicating that the more complex original pattern was due to interactions between out of phase ampullae. Ampullae and associated vessels might be analogous with the system of lymphatic vessels in vertebrates.

Fear Induced Multistability in a Predator-Prey Model

In ecology, the predator’s impact goes beyond just killing the prey. In the present work, we explore the role of fear in the dynamics of a discrete-time predator-prey model where the predator-prey interaction obeys Holling type-II functional response. Owing to the increasing strength of fear, the system becomes stable from chaotic oscillations via inverse Neimark–Sacker bifurcation. Extensive numerical simulations are carried out to investigate the intricate dynamics for the organization of periodic structures in the bi-parameter space of the system. We observe fear induced multistability between different pairs of coexisting heterogeneous attractors due to the overlapping of multiple periodic domains in the bi-parameter space. The basin sets of the coexisting attractors are obtained and discussed at length. Multistability in the predator-prey system is important because the dynamics of the predator and prey populations in the critical parameter zone becomes uncertain.

Sliding Mode Control for Chaotic Oscillations in SMIB Power System

Power systems may revelation the harmful and undesirable chaotic phenomenon in certain conditions. This project describes the control of a chaotic oscillation in power system. Chaos may lead the power system to voltage instability and voltage collapse when voltage stability conditions are broken. Chaotic oscillations are very sensitive to parameter and initial conditions of power system. Many controllers are projected in practical to suppress the chaos and avoid voltage collapse. In this thesis, a Conventional Sliding Mode Control is applied for removal of chaotic oscillations. The aim of the controller is to remove the chaotic oscillations and bring the order to the nonlinear system. It is also shown that the proposed controller assurances the system state convergence to their desired ethics. To demonstrate the effectiveness of the projected controller, MATLAB Programming is done. Keywords: Chaotic oscillations, SMIB, Conventional Sliding Mode Control

Investigating the Cocaine-induced Reduction of Potassium Current on the Generation of Action Potentials Using a Computational Model

Introduction: Drugs of abuse, including cocaine, affect different brain regions and lead to pathological memories. These abnormal memories may occur due to the changes in synaptic transmissions or variations in synaptic properties of neurons. It has been shown that cocaine inhibits delayed rectifying potassium currents in affected regions of the brain and can have a role in the formation of pathological memories. Purpose: This study investigates how the change in the conductance of delayed rectifying potassium channels can affect the produced action potentials using a computational model. Methods: We present a computational model with different channels and receptors, including sodium, potassium, calcium, NMDARs, and AMPARs, which can produce burst-type action potentials. In the simulations, by changing the delayed rectifying potassium conductance bifurcation diagram is calculated. Conclusion: Results show that for a specific range of potassium conductance, a chaotic regime emerges in produced action potentials. These chaotic oscillations may play a role in inducing abnormal memories.

Finite-Time Impulsive Control of Financial Risk Dynamic System with Chaotic Characteristics

The control of financial risk has always been one of the important topics in financial research. Based on the theory of finance, this paper proposes a kind of financial risk dynamic system. By analyzing some properties of the dynamic system, the system shows obvious coexisting chaotic oscillations. In order to control the financial risk dynamic system effectively, this paper proposes a finite-time impulse controller to control the financial risk dynamic system. Simulation results show that the finite-time impulse controller has faster convergence speed than the impulse controller.