Dynamical control in multistable systems

Technical Physics Letters - The possibility of controlling oscillatory regimes in a dynamical system in which multistability is observed for certain values of the control parameters is considered...     

立方非线性包装系统在基础振动激励下的响应

对振动环境中立方非线性包装系统进行了计算机仿真及分析,通过对系统响应的时间历程、相图、Poincare映射及功率谱等的分析,讨论了在确定性振动环境中包装系统的动力学行为,并讨论了控制响应的措施.     

分段线性运输包装振动系统的研究

对振动环境中分段线性运输包装系统进行了计算机仿真及分析,通过对系统运动的时间历程、相图、Poincare映射及功率谱等的分析,讨论了在确定性振动环境中系统的混沌动力学行为,并进一步给出了混沌控制措施.     

Analysis of radiative heat-loss effects in thermal explosion of a gas using the integral manifold method

Semenov's classical model of thermal explosion in a combustible gas mixture is modified to include radiative (rather than conductive) heat-loss effects and gas-density changes. A geometrical asymptotic technique (the method of integral manifolds - MIM) is exploited to perform a qualitative analysis of the governing equations. The strength of this method lies in the compact, clear geometrical/analytical rendition and classification of all possible dynamical scenarios, in terms of the physico-chemical parameters of the system. It is found that there are two main dynamical regimes of the system: cooling regimes and fast explosive regimes. Peculiarities of these dynamical regimes are investigated and their dependence on physical system parameters is analyzed. A criterion for the occurrence of thermal explosion is disclosed. An estimate for the maximum mixture temperature is also derived analytically. It is found that, under certain operating conditions, the dynamics are such that the initial explosive stage of the process essentially behaves adiabatically before succumbing to the dominance of the radiative heat loss that brings the system down to the ambient temperature.     

A dynamic model for a thermostat

A new mathematical model for the dynamic behavior of a thermostat situated in the cooling system of an engine is presented. The model is in the form of a system of delay-differential equations with hysteresis. An algorithm for numerical solutions of the model is described and some representative simulations are presented. The model predicts steady oscillatory solutions for certain ranges of the system parameters which are depicted for some parameter values. Also, it predicts initial overshooting of the engine coolant temperature. A Design of Experiments approach is used to characterize the regions in the model parameter space where oscillations occur and the results for those parameters which most influence the oscillations of solutions are presented.     

Vibration reduction in a step motor using optimal control time intervals and amplitudes

Summary This paper deals with the optimal vibration elimination technique and the experimental demonstration of a cylindrical linear step motor dynamic behavior. Electrical, mechanical and magnetic motion equations are used to analyze the system behavior, employing a general-purpose method and finite element method. The oscillatory transient region of the step response and the inertial effect of the mover are investigated. The influence of the command time between steps and amplitude of commands on the damping capacity is determined. Thus, the optimal command time interval and amplitude degrees are found that remove the vibration completely in the least time. A comparison of the theory with the measured results shows the validity of this analysis.     

On the existence of periodic solution for equation of motion of thick beams having arbitrary cross section with tip mass under harmonic support motion

A cantilever beam having arbitrary cross section with a lumped mass attached to its free end while being excited harmonically at the base is fully investigated. The derived equation of vibrating motion is found to be a non-linear parametric ordinary differential equation, having no closed form solution for it. We have, therefore, established the sufficient conditions for the existence of periodic oscillatory behavior of the beam using Green’s function and employing Schauder’s fixed point theorem. The derived equation of vibration motion is found to be a non-linear parametric ordinary differential equation, having no closed form solution for it. To formulate a simple, physically correct dynamic model for stability and periodicity analysis, the general governing equations are truncated to only the first mode of vibration. Using Green’s function and Schauder’s fixed point theorem, the necessary and sufficient conditions for periodic oscillatory behavior of the beam are established. Consequently, the phase domain of periodicity and stability for various values of physical characteristics of the beam-mass system and harmonic base excitation are presented.     

Bifurcation analysis of bistable and oscillatory dynamics in biological networks using the root‐locus method

Most of the biological systems including gene regulatory networks can be described well by ordinary differential equation models with rational non‐linearities. These models are derived either based on the reaction kinetics or by curve fitting to experimental data. This study demonstrates the applicability of the root‐locus‐based bifurcation analysis method for studying the complex dynamics of such models. The effectiveness of the bifurcation analysis in determining the exact parameter regions in each of which the system shows a certain dynamical behaviour, such as bistability, oscillation, and asymptotically equilibrium dynamics is shown by considering two mostly studied gene regulatory networks, namely Gardner''s genetic toggle switch and p53 gene network possessing two‐phase (mono‐stable/oscillation) dynamics.Inspec keywords: oscillations, curve fitting, differential equations, bifurcation, genetics, nonlinear dynamical systemsOther keywords: nonlinearities, reaction kinetics, root‐locus‐based bifurcation analysis method, complex dynamics, exact parameter regions, dynamical behaviour, equilibrium dynamics, studied gene regulatory networks, p53 gene network, bistable dynamics, oscillatory dynamics, biological networks, root‐locus method, biological systems, ordinary differential equation models     

Reduced model of discrete‐time dynamic image segmentation system and its bifurcation analysis

We have developed a discrete‐time dynamic image segmentation system consisting of chaotic neurons and a global inhibitor. Our system receives an image with isolated regions and can output segmented images in time series based on oscillatory responses of chaotic neurons. In this article, we derive a reduced model to find intrinsic properties of the system of dynamic image segmentation. Using numerical method for analyzing dynamical systems, we investigated bifurcation phenomena of a fixed point observed in the reduced model. As the results, in a model of two coupled chaotic neurons, we found that a set of Neimark‐Sacker bifurcations causes the generation of an in‐phase oscillatory response, which is unsuitable for the purpose of dynamic image segmentation. The bifurcation analysis gives appropriate parameter values to exclude the generation of in‐phase oscillatory responses, i.e., our dynamic image segmentation system can work well. © 2009 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 19, 283–289, 2009     

Computer Methodologies for the Comparison of Some Efficient Derivative Free Simultaneous Iterative Methods for Finding Roots of Non-Linear Equations

In this article, we construct the most powerful family of simultaneous iterative method with global convergence behavior among all the existing methods in literature for finding all roots of non-linear equations. Convergence analysis proved that the order of convergence of the family of derivative free simultaneous iterative method is nine. Our main aim is to check out the most regularly used simultaneous iterative methods for finding all roots of non-linear equations by studying their dynamical planes, numerical experiments and CPU time-methodology. Dynamical planes of iterative methods are drawn by using MATLAB for the comparison of global convergence properties of simultaneous iterative methods. Convergence behavior of the higher order simultaneous iterative methods are also illustrated by residual graph obtained from some numerical test examples. Numerical test examples, dynamical behavior and computational efficiency are provided to present the performance and dominant efficiency of the newly constructed derivative free family of simultaneous iterative method over existing higher order simultaneous methods in literature.     

热冲击下的复合材料壳刚柔耦合动力学研究

研究了在热冲击下任意形状(仅一个方向有曲率)复合材料壳的非线性刚柔耦合动力学响应。根据Mindlin理论,建立了任意形状的复合材料壳的非线性应变-位移关系。借助于数学理论以及几何关系,描述了壳上任意点的变曲率。用虚功原理建立了动力学变分方程,并采用等参单元对壳的连续动力学方程进行离散,建立了中心刚体-复合材料壳的刚-柔耦合动力学方程。用高斯积分计算常值阵,为了提高计算效率,采用广义-α法结合Newton-Raph-son迭代法对动力学方程进行积分。将采用该方法计算得到的频率与ANSYS软件计算得到的作对比,验证了模型的正确性。通过算例分析了在热冲击作用下复合材料壳的线性、非线性的动力学特性,以及曲率、材料特性对动力学响应的影响。     

A vorticity-only formulation and a low-order asymptotic expansion solution near Hopf bifurcation

A vorticity-only formulation is used in order to study the behavior of the solutions of the Navier-Stokes equations for two-dimensional incompressible flows as the Reynolds number is increased. This approach allows one to limit the numerical-solution domain to the vortical region of the flow, thereby reducing the number of the state variables of the system. The vorticity-only formulation is obtained from a vorticity-stream function formulation by inverting the Poisson equation relating the vorticity to the stream function and substituting the expression for the velocity in the vorticity-transport equation. The vorticity at the solid boundary is determined from the boundary conditions. The resulting dynamical system consists of a set of first-order ordinary differential equations having only quadratic nonlinearities. This system is then used to address the behavior of the solution beyond the stability boundary, within the context of the theory of dynamical systems. This part of the paper is general and is based on the use of a singular-perturbation technique, known as the method of multiple time scales; formulae for the nonlinear analysis near a Hopf bifurcation are given explicitly in terms of the coefficients of the dynamical system. Preliminary numerical results for the validation of the formulation are presented for the limited case of two-dimensional flows around a circular cylinder. These results include the steady-state solution with varying Reynolds number, the eigenvalues and the eigenvectors of the related stability matrix, and the characteristics of the corresponding limit cycle.     

Dynamical Analysis of Rub-impact Rotor System with Asymmetric Oil Film Force

Considering the effect of non-symmetry film force,nonlinear stiffness and nonlinear friction force,a dynamical model of rub-impact rotor system is established,then the nonlinear dynamical behavior is studied by numerical analysis method.The effect of rotation speed,nonlinear stiffness ratio and speed effect factor on brifurcation and chaotic behavior for rub-impact rotor system is comprehensively analyzed.The analysis results show that the effect of non-symmetry film force,nonlinear stiffness and nonlinear friction force on the dynamical behavior of the rotor system has close relation with rotation speed.The chaotic behavior exists in a wider parameter region,and the chaotic evolution rule is more complicated.The research provides a reliable theory basis and reference for diagnosing some faults of the rotor system.     

On the analysis of hopf bifurcations

The oscillatory instability and the family of limit cycles associated with a general autonomous dynamical system described by $\text{n}$ nonlinear first order differential equations and an independently assignable scalar parameter are examined via an intrinsic method of harmonic analysis. The method is essentially a variation of the classical method of “harmonic balancing”, and is designed to eliminate the drawbacks and shortcomings associated with the latter. Indeed, the new approach yields consistent approximations for the nonlinear dynamical bifurcation problem under consideration through a systematic perturbation procedure. It has thus been possible to derive explicit, formula-type expressions for the post-critical family of the periodic solutions, frequency of oscillations and the path which represents the family bifurcating from a flutter-critical point on an initially stable equilibrium path. The results are available to be used directly in the analysis of specific problems which fall within the scope of the formulation, without actually performing much analysis. Two illustrative examples are provided.     

On the construction of a dynamical system from a preassigned family of solutions

This article deals with the determination of the forces in a dynamical system, when the general form of the solution is given. This makes it possible to construct a system with a predetermined type of behavior. It is shown that the problem generally requires the solution of a partial differential equation. The method of constraints and Lagrange multipliers is used to derive this equation. The relation with some older results (Dainelli's formulas) is shown. As an illustration of the application of the method, the partial differential equation is solved for a family of potentials that result in oscillatory motions on a parabolic curve. A simple integrable system is first constructed, generalizing free-fall motion on a parabolic path. A more complex solution of the partial differential equation is then used to construct a fairly complex dynamical system with 2 degrees-of-freedom. This system has been studied in some detail with numerical methods. In particular, the periodic oscillations of the system are classified and their characteristic exponents and bifurcations are studied.     

Mucoadhesive nanoliposomal formulation for vaginal delivery of an antifungal

Context: Ciclopirox olamine (CPO) is indicated in the treatment of vaginal fungal infections. The frequent and large dosing of available vaginal CPO creams gives rise to poor compliance amongst females. In such a situation a delivery system capable of providing sustained release of CPO is warranted and can be realized through incorporation of its liposomal formulation into a mucoadhesive gel base. The liposomal formulation would offer sustained release whereas mucoadhesive gel would prolong the contact with vaginal wall; thus avoiding frequent and large dosing.

Objective: The present study aimed at investigating mucoadhesive liposomal CPO gel for vaginal use.

Method: The study embarked on evaluating liposomal CPO and its Carbopol 974^®P gel for stability at vaginal pH, release profile, rheological characteristics, mucoadhesive behavior and finally antifungal activity.

Results: The results revealed that CPO liposomes were stable at vaginal pH; its Carbopol gel released 58.75?±?6.4% of CPO at the end of 24?h which suggested sustained release. Rheology via viscometric, oscillatory stress sweep and oscillatory frequency sweep testing of the gel, studied at different temperatures and under different dilutions with vaginal fluid simulant testified pseudoplastic behavior of the gel. It also pointed towards the predominance of elastic behavior of the gel at all the dilutions. The gel exhibited good mucoadhesivity to sheep vaginal tissue. Furthermore, CPO entrapped in liposome too displayed antifungal activity.

Conclusion: The study undertaken recommended Carbopol 974^®P gel loaded with CPO liposomes as a potential delivery system for treatment of fungal vaginal infections.     

Analysis of static non-linear response by explicit time integration

In general, a system of linear (or non-linear) algebraic equations is solved on an analogue computer by integrating an appropriately defined system of associated first-order differential equations, the steady-state solution of which is the desired solution of algebraic system. This approach usually works very well so long as the associated dynamical system is stable. The idea of using the same approach numerically is also not altogether new. One can, ‘analogously’, construct a dynamical system associated with a given system of non-linear algebraic equations and solve it numerically by any of a number of explicit time integration schemes. In fact, similar ideas provide the basis for certain ‘dynamic relaxation’ methods, incremental loading methods and the widely acclaimed methods of invariant imbedding.     

带强迫项的非线性高阶中立型方程解的渐进性和振动性

本文给出了带强迫项的非线件高阶中立型方程解的渐进性和振动性的三个充分条件,同时还得到了该方程所有无界解振动的一个充分条件。     

Vortex Configurations in a Mesoscopic Superconducting Ring Structure: A Finite-Element Analysis

The time-dependent Ginzburg–Landau equations have been solved numerically by a finite-element analysis for a mesoscopic superconducting ring structure. For given applied magnetic fields we have simulated the dynamical behavior of the penetrating magnetic vortices into the superconductor. Moreover, we investigated the vortex configurations and found a vortex state with two stable vortex shells in the mesoscopic superconducting ring due to the enhanced surface superconductivity.     

Controlling attractor structure in bistable chaotic oscillator

The effect of the asymmetric characteristic of a nonlinear element in the Chua oscillator on the oscillatory process in this chaotic dynamical system has been studied. The system behavior was studied under the action of irregular oscillations modeling the intrinsic noise, rather than as excited by a single impact. It is established that a growth in the asymmetry parameter of the nonlinear element characteristic leads to an asymmetry of the chaotic attractor of the Chua oscillator that maps the switching of motions between the two basins of attraction. Then, the system exhibits a bifurcation, whereby chaotic oscillations arise in one of these basins and develop into motions that correspond to a multiple limit cycle.