Mathematical models and stabilizing bio-control mechanisms for microbial populations in a cultured environment

In this paper we have analyzed a limited nutrient–consumer dynamic model involving distributed time delays both in material recycling and growth response of consumer. It is established that the system exhibits instability characteristics due to the presence of time delays. Three different types of naturally feasible bio-control mechanisms are proposed. It is established that these mechanisms have a stabilizing effect on the system in their own respect. Several independent sets of sufficient conditions for the global asymptotic stability are obtained in each case. Examples and simulations are provided for a clear understanding of the results.     

A generalization of Lotka–Volterra,GLV, systems with some dynamical and topological properties

It is shown that local asymptotic instability is related to the existence of a positive Lyapunov exponent which is a necessary condition for chaos. Also it is proved that linear transformations do not affect the dynamical behaviour of the system. A generalized Lotka–Volterra (GLV) model is introduced and proved that for specific choices of parameters it exhibits chaos. Knots and links which arise from the system which describe the behaviour of a typical nuclear spin are studied. We conjecture that knots and links associated GLV is much more general than Lorenz knots, and the one predator – two preys LV model exhibits chaos for general parameters.     

Bifurcation analysis of a diffusive predator–prey system with a herd behavior and quadratic mortality

In this paper, a diffusive predator–prey system, in which the prey species exhibits herd behavior and the predator species with quadratic mortality, has been studied. The stability of positive constant equilibrium, Hopf bifurcations, and diffusion‐driven Turing instability are investigated under the Neumann boundary condition. The explicit condition for the occurrence of the diffusion‐driven Turing instability is derived, which is determined by the relationship of the diffusion rates of two species. The formulas determining the direction and the stability of Hopf bifurcations depending on the parameters of the system are derived. Finally, numerical simulations are carried out to verify and extend the theoretical results and show the existence of spatially homogeneous periodic solutions and nonconstant steady states. Copyright © 2014 John Wiley & Sons, Ltd.     

System Dynamics in Shipping

A system which exhibits time-varying fluctuations in measures which describe its state and which comprises inter-dependent feedback loops is likely to be amenable to the modelling methods of system dynamics. The shipping industry is analysed from this point of view with the aim of identifying its dynamic characteristics and their causal mechanisms. Examples are given of observed dynamic behaviour within and between trade sectors.     

永磁同步电动机中的混沌现象

讨论永磁同步电动机（PMSM）的动态特性,给出常输入电压、常外部扭转条件下的系统稳态特性表达式,基于Hopf分支条件提出一种调节系统参数的方法,以使其呈现极限环或混沌行为。计算机仿真结果表明在永磁同步电动机中存在混沌现象。     

基于自组织理论的技术创新系统演化机理及模型分析

创新是人类财富之源,是经济发展的巨大动力。本文从复杂系统理论角度说明了技术创新系统的自组织特性;分析了创新过程的不稳定性、分岔、突变和随机"涨落"等演化特征和作用机理;随后结合进化经济学理论,构建了技术创新系统自组织竞争与协同演化过程的定量模型,并对模型的稳定性和演化趋势进行分析,应用统计和数学工具软件对模型的参数变化进行函数模拟,对模拟结果进行了讨论;随后以我国通信产业发展为例进行了相关案例分析。此研究旨在通过自然科学与社会科学的有效结合,对技术创新系统的演化机理及过程提供一种新的研究思路。     

非对称开采时矿柱失稳的尖点突变模型

针对非对称开采时矿柱稳定性问题建立了一个简化的力学模型．基于势能原理,应用尖点突变理论对矿柱成为非稳定系统进行了探讨,导出了失稳的充要条件、矿柱变形突跳量和能量释放表达式,为定量研究其失稳问题奠定了基础．结果表明:系统的失稳不仅与其所受载荷有关,而且与其内部刚度分配有关,当相对刚度值越大,所承受的临界载荷也越大,越不容易失稳．反之,越容易失稳,且失稳时所释放的能量越大,危害也越大．给出了算例,其计算结果可为安排开采顺序、合理布置采场等提供依据．     

Stability analysis of combustion waves for competitive exothermic reactions using Evans function

We consider travelling wave solutions of a reaction-diffusion system corresponding to an adiabatic two-step competitive exothermic reaction scheme. In such a scheme, a combustion process is assumed to be lumped into two different exothermic reactions. Although the rate constants of the reactions are distinct, both reactions occur simultaneously and feed on the same reactant. The travelling wave solutions are obtained via the shooting-relaxation method. The linear stability analysis is conducted using the Evans function technique and the compound matrix method. Further, threshold values of parameters corresponding to Hopf points are established. It is shown that the system exhibits pulsating behaviour when the parameter values are greater than the threshold values. The onset of instability is found for a broad range of parameter values. Two different numerical methods are then used to obtain solutions from the governing partial differential equations to validate the results.     

Stability Analysis of Stationary Light Transmission in Nonlinear Photonic Structures

We study optical bistability of stationary light transmission in nonlinear periodic structures of finite and semi-infinite length. For finite-length structures, the system exhibits instability mechanisms typical for dissipative dynamical systems. We construct a Leray-Schauder stability index and show that it equals the sign of the Evans function in = 0. As a consequence, stationary solutions with negative-slope transmission function are always unstable. In semi-infinite structures, the system may have stationary localized solutions with nonmonotonically decreasing amplitudes. We show that the localized solution with a positive-slope amplitude at the input is always unstable. We also derive expansions for finite size effects and show that the bifurcation diagram stabilizes in the limit of the infinite domain size.     

Chaotic effects on disease spread in simple eco-epidemiological system

In this paper, an eco-epidemiological model where prey disease is structured as a susceptible-infected model is investigated. Thresholds that control disease spread and population persistence are obtained. Existence, stability and instability of the system are studied. Hopf bifurcation is shown to occur where a periodic solution bifurcates from the coexistence equilibrium. Simulations show that the system exhibits chaotic phenomena when the transmission rate is varied.     

Amplitude Instability in Coupled Nd:YVO4Microchip Lasers

A system of two coupled Nd:YVO₄ microchip lasers exhibits a phaselocking instability as coupling strength or mutual detuning are varied across the phase-lockingthresholds. The compact semi-monolithic resonator setup enables investigations in a regime ofvery small detuning. Time-resolved measurements reveal the correlation between the onset ofintensity pulsations and phase locking.     

Sawtooth disruptions and limit cycle oscillations

A minimal (low-dimensional) dynamical model of the sawtooth oscillations is presented. It is assumed that the sawtooth is triggered by a thermal instability which causes the plasma temperature in the central part of the plasma to drop suddenly, leading to the sawtooth crash. It is shown that this model possesses an isolated limit cycle which exhibits relaxation oscillation, in the appropriate parameter regime, which is the typical characteristics of sawtooth oscillations. It is further shown that the invariant manifold of the model is actually the slow manifold of the relaxation oscillation.     

Parameter Estimation of the Disk in a Floating Caliper Disk Brake Model with respect to Squeal

Noise from a vehicle is always a concern for any automotive industry looking for passenger comfort. This also holds for the different types of brake noise, in particular for squeal, which is a source of discomfort both to passengers and passers‐by. Intensive research on low frequency squeal (noise between 1‐5 kHz) has been carried out. A model of the floating caliper disk brake has been recently proposed by the authors with the aim to predict the onset of squeal. A flutter type instability resulting from nonconservative restoring forces is assumed to be the reason behind squeal in this model. The problem of validating the model against experimental observation lies in the fact that all the system parameters included in the model, especially the disk, are to be carefully chosen. In this work some parameters of the disk are estimated and a method is suggested to estimate these parameters in a systematic way. For that purpose, the values are to be accurately selected by experiments and modal updating technique. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the influence of the lamella's elasticity on self-excited vibrations in gearboxes

Eek noise in a gearbox of a vehicle drivetrain is a phenomenon, which can arise while shifting between gears and which is not accepted by customers. Beneath audible squeaking, it can cause damage of mechanical components. There is a wide range of possible reasons for the occurrence of this effect, which strongly depends on properties of the considered gearbox (physical parameters, geometry, operation, …). From the mathematical point of view, the occurrence can be predicted using linear stability analysis of the stationary behaviour of a physically motivated gearbox model. The components of a gearbox are clutch discs being in contact, gears and elastically supported shafts. In this contribution, a rigid multibody model of the device [4] is extended by the elastic modelling of the motor's side disc (rotating Kirchhoff plate). The aim of the overall system is to analyze the shifting process. The analysis reveals that beneath instability mechanisms which are known from systems with rigid bodies, new instabilities occur incorporating of out-of-plane vibrations of the plate. In a reasonable parameter region, the first two unsymmetrical modes of the lamella have the main contribution to the instability. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

波浪、海洋土参数对海床稳定性影响

基于Yamamoto的多孔弹性介质模型,研究了波生底床的稳定性.通过给出的有限深底床下土响应分析解,针对三种土质底床,讨论了主要波参数和土参数对这些底床稳定性的影响.与其他土模型计算结果进行了比较,分析了海洋土内部Coulomb摩擦因素的影响.     

Analysis and circuitry realization of a novel three-dimensional chaotic system

In this paper a new three-dimensional chaotic system is introduced. Some basic dynamical properties are analyzed to show chaotic behavior of the presented system. These properties are covered by dissipation of system, instability of equilibria, strange attractor, Lyapunov exponents, fractal dimension and sensitivity to initial conditions. Through altering one of the system parameters, various dynamical behaviors are observed which included chaos, periodic and convergence to an equilibrium point. Eventually, an analog circuit is designed and implemented experimentally to realize the chaotic system.     

Adaptive estimation of nonlinear parameters of a nonholonomic spherical robot using a modified fuzzy-based speed gradient algorithm

This paper deals with adaptive estimation of the unknown parameters and states of a pendulum-driven spherical robot (PDSR), which is a nonlinear in parameters (NLP) chaotic system with parametric uncertainties. Firstly, the mathematical model of the robot is deduced by applying the Newton–Euler methodology for a system of rigid bodies. Then, based on the speed gradient (SG) algorithm, the states and unknown parameters of the robot are estimated online for different step length gains and initial conditions. The estimated parameters are updated adaptively according to the error between estimated and true state values. Since the errors of the estimated states and parameters as well as the convergence rates depend significantly on the value of step length gain, this gain should be chosen optimally. Hence, a heuristic fuzzy logic controller is employed to adjust the gain adaptively. Simulation results indicate that the proposed approach is highly encouraging for identification of this NLP chaotic system even if the initial conditions change and the uncertainties increase; therefore, it is reliable to be implemented on a real robot.     

On a measure of the closeness of neutral systems to internal resonance

For certain classes of parametrically perturbed resonance systems that are neutral in a linear approximation, a quantitative characteristic is introduced for the closeness of the system of resonance: the magnitude of the critical detuning value for resonance δ* at which the change in stability occurs as the system withdraws from resonance. The problem of finding this critical value is made complicated by the non-linear nature of the change in stability in neutral systems. It is solved below for third-order resonances in a situation that guarantees the passage of instability into asymptotic stability as the system withdraws from resonance.

Knowledge of the quantity δ* enables the strong instability domain /1, 2/ in parameter space to be estimated, enables the danger of resonance to be characterized, and enables the structural parameter in the system, the shift of the resonance phases, to be clarified, whose variation would enable the danger of resonance to be increased or reduced.     

Stability and Hopf bifurcation of a diffusive predator–prey model with predator saturation and competition

This article discusses a predator–prey system with predator saturation and competition functional response. The local stability, existence of a Hopf bifurcation at the coexistence equilibrium and stability of bifurcating periodic solutions are obtained in the absence of diffusion. Further, we discuss the diffusion-driven instability, Hopf bifurcation for corresponding diffusion system with zero flux boundary condition and Turing instability region regarding the parameters are established. Finally, numerical simulations supporting the theoretical analysis are also included.     

Influence of the contact model on the onset of sprag-slip

In systems with sliding-friction often strong self-excited vibrations do occur. One of the possible underlying mechanisms is the so-called sprag-slip instability. In the present work the onset of sprag-slip is investigated by a simple model in which an inclined elastic beam slides over a rigid belt moving with constant velocity. For a Coulomb friction law and a contact model with constant contact stiffness for a certain range of parameters the system loses its static solution corresponding to the steady sliding state. Simultaneously with this loss of existence of the static solution the qualitative properties of the system's flow field in phase space change, resembling a transition from stable to unstable behavior. To investigate the influence of contact models and related parameters on the details of this onset of sprag-slip also Hertz theory of elastic contact is applied. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)