Stopping checks in a system with two degrees-of-freedom and friction-affected constraints governed by both generalized co-ordinates

Summary A multi-body system with two degrees-of-freedom and several friction-affected constraints is considered. It is supposed that the original system and all systems, which must be considered as result of sticking co-ordinates, are kinetostatical determinate structures. The case is analysed, when several friction-affected constraints are governed by both generalized co-ordinates. The accelerations of the system, when relative velocities in several or all friction-affected constraints vanish, are determined with a trial- and -error method based on Lagrange's equations of the second kind and conditions of dynamic equilibrium. Computations for particular systems revealed numerical particularities, which are helpful in reducing the necessary number of trials.

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Zusammenfassung Ein Mehrkörpersystem mit zwei Freiheitsgraden und mehreren reibungsbehafteten Bindungen wird betrachtet und angenommen, daß dieses System und alle Systeme, die zu berücksichtigen sind, wenn in einigen Bindungen Haften auftritt, kineto-statisch bestimmt sind. Es wird der Fall untersucht, wenn die Lageparameter einiger reibungsbehafteter Bindungen von beiden verallgemeinerten Koordinaten abhängen. Mit einem trial- and -error Verfahren werden die Beschleunigungen des Systems bestimmt, wenn die Relativgeschwindigkeiten in einigen oder allen reibungsbehafteten Bindungen gleich Null sind. Dazu werden die Lagrangeschen Gleichungen zweiter Art und die dynamischen Gleichgewichtsbedingungen verwendet. Berechnungsbeispiele offenbarten numerische Besonderheiten, die zur Verringerung der Anzahl der notwendingen Tests beitragen.

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Dedicated to Professor Dr. G. Schmidt, Berlin, on the occasion of his 65th birthday.     

Periodic motions in a simplified brake system with a periodic excitation

In this paper, periodic motions for a simplified brake system under a periodical excitation are investigated, and the motion switchability on the discontinuous boundary is discussed through the theory of discontinuous dynamical systems. The onset and vanishing of periodic motions are discussed through the bifurcation and grazing analyses. Based on the discontinuous boundary, the switching planes and the basic mappings are introduced, and the mapping structures for periodic motions are developed. From the mapping structures, the periodic motions are analytically predicted and the corresponding local stability and bifurcation analysis is completed. Periodic motions will be illustrated for verification of analytical predictions. In addition, the relative force distributions along the displacement are illustrated for illustrations of the analytical conditions of motion switchability on the discontinuous boundary.     

Bifurcations of periodic solutions and chaos in Josephson system with parametric excitation

Josephson system with parametric excitation is investigated. Using second-order averaging method and Melnikov function, we analyze the existence and bifurcations for harmonic,(2, 3, n-order) subharmonics and(2, 3-order) superharmonics and the heterocilinic and homoclinic bifurcations for chaos under periodic perturbation. Using numerical simulation, we check our theoretical analysis and further study the effect of the parameters on dynamics. We find the complex dynamics, including the jumping behaviors, symmetrybreaking, chaos converting to periodic orbits, interior crisis, non-attracting chaotic set, interlocking(reverse)period-doubling bifurcations from periodic orbits, the processes from interlocking period-doubling bifurcations of periodic orbits to chaos after strange non-chaotic motions when the parameter β increases, etc.     

Steady state scheduling of a flexible manufacturing system with periodic releasing and flow time constraints

This paper deals with the dynamic behaviour of an FMS when parts are released periodically. The minimal release period is induced by the most critical machine or fixture pallet type. Moreover, with a fixed period, the limited number of available pallets induces a maximal flow time for every part type. Thus, the objective of this paper is to determine a part release strategy and an activity schedule on every machine which allows to control every part flow time for steady state. An analysis method for this objective is presented in this paper. Its purpose is to obtain releasing and scheduling conditions ensuring a workshop steady state compatible with the considered constraints, especially part flow times. This method is based on the resolution of conflicts between activities processed on a common machine. This resolution uses limit times associated with each activity and it can modify these limit times. These modifications in turn can induce modifications for other activity limit times due to part routing, steady-state periodicity, and part flow time constraints. Thus, an iterative procedure has been defined. It refines steady-state feasibility conditions through limit times and sequencing conditions of activities processed on a common machine. The method is illustrated with two examples.     

Dispersal permanence of a periodic predator-prey system with Holling type-IV functional response

In this paper, we study the permanence of a class of periodic predator-prey system with Holling type-IV functional response where the prey disperses in patchy environment with two patches, and provide a sufficient and necessary condition to guarantee permanence of the system. Finally, two examples are presented to illustrate the application of our main results.     

Existence of periodic solutions to a system with functional response on time scales

This paper investigates the existence of periodic solutions of a three-species food-chain diffusive system with Beddington-DeAngelis functional responses and time delays in a two-patch environment on time scales. By using a continuation theorem based on coincidence degree theory, we obtain sufficient criteria for the existence of periodic solutions for the system. Moreover, when the time scale T is chosen as R or Z, the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the method is unified to provide the existence of the desired solutions for continuous differential equations and discrete difference equations.     

The Gibbs' phenomenon and harmonic oscillators with periodic forcing

We present an interesting nonlinear equation originating from a geometrical problem. We show how it can be solved numerically, how algorithmic differentiation is useful, and how the problem can also be solved analytically using the computer algebra system Maple.     

具有Holling功能反应的非自治捕食系统的持续性和周期解

研究了具有一般的Holling功能反应函数,且种群之间既有捕食关系,又有竞争关系的三种群混合模型,得到了该系统惟一存在全局渐近稳定正周期解的条件,推广了已有结论.     

Chaos control by harmonic excitation with proper random phase

Chaos control may have a dual function: to suppress chaos or to generate it. We are interested in a kind of chaos control by exerting a weak harmonic excitation with random phase. The dual function of chaos control in a nonlinear dynamic system, whether a suppressing one or a generating one, can be realized by properly adjusting the level of random phase and determined by the sign of the top Lyapunov exponent of the system response. Two illustrative examples, a Duffing oscillator subject to a harmonic parametric control and a driven Murali-Lakshmanan-Chua (MLC) circuit imposed with a weak harmonic control, are presented here to show that the random phase plays a decisive role for control function. The method for computing the top Lyapunov exponent is based on Khasminskii's formulation for linearized systems. Then, the obtained results are further verified by the Poincare map analysis on dynamical behavior of the system, such as stability, bifurcation and chaos. Both two methods lead to fully consistent results.     

具脉冲效应和Beddington-DeAnglis功能反应时滞周期捕食系统

研究一类具有脉冲效应和Beddington-DeAnglis功能反应的时滞周期捕食系统,给出系统持续生存和周期解存在的条件.证明了在无时滞情况下,周期解是全局稳定的.     

Permanence, extinction and periodic solution of predator-prey system with Beddington-DeAngelis functional response

In this paper we study permanence, extinction and periodic solution of periodic predator-prey system with Beddington-DeAngelis functional response. We provide a sufficient and necessary condition to guarantee the predator and prey species to be permanent. In addition, sufficient condition is derived for the existence of positive periodic solution. This paper improves some main results obtained by Fan and Kuang [M. Fan, Y. Kuang, Dynamics of nonautonomous predator-prey system with the Beddington-DeAngelis functional response, J. Math. Anal. Appl. 295 (2004) 15-39].     

Positive periodic solution for a multispecies competition-predator system with Holling III functional response and time delays

In this paper, a delayed multispecies ecological competition-predator system with Holling-III functional response is studied. By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functionals, some sufficient conditions are derived for the existence, uniqueness and global asymptotic stability of positive periodic solutions to the system.     

Existence of periodic solutions for a predator-prey system with sparse effect and functional response on time scales

In this paper, we systematically investigates the existence of periodic solutions of a predator-prey system with sparse effect and Beddington-DeAngelis or Holling III functional response on time scales. By using a continuation theorem based on coincidence degree theory, we obtain sufficient criteria for the existence of periodic solutions for the systems. Moreover, when the time scale T is chosen as R or Z, the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the methods are unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations.     

Evolutionary dynamics of a system with periodic coefficients

We investigate a problem in evolutionary game theory based on replicator equations with periodic coefficients. This approach to evolution combines classical game theory with differential equations. The RPS (Rock-Paper-Scissors) system studied has application to the population biology of lizards and to bacterial dynamics. The presence of periodic coefficients models variations in the environment due to seasonal effects and results in parametric excitation which is studied through the use of perturbation series and numerical integration.     

Stability of bifurcating periodic solutions for a single delayed inertial neuron model under periodic excitation

Using the averaged method, we investigate the dynamical characteristics of a single inertial neuron model with time delay under periodic external stimuli. It is shown that the system will lose its stability when the time delay is increased and will give rise to a quasi-periodic motion and chaos under the interaction of the periodic excitation. Numerical simulations show that the results of the analytical method are correct by a comparison with those of direct numerical integration.     

Homogenization of integrals with pointwise gradient constraints via the periodic unfolding method

Abstract The pointwise gradient constrained homogenization process, for Neumann and Dirichlet type problems, is analyzed by means of the periodic unfolding method recently introduced in [21]. Classically, the proof of the homogenization formula in presence of pointwise gradient constraints relies on elaborated measure theoretic arguments. The one proposed here is elementary: it is based on weak convergence arguments in L^p spaces, coupled with suitable regularization techniques. Keywords: Homogenization, Gradient constrained problems, Periodic unfolding method Mathematics Subject Classification (2000): 49J45, 35B27, 74Q05     

An easy trick to a periodic solution of relativistic harmonic oscillator

In this paper, the relativistic harmonic oscillator equation which is a nonlinear ordinary differential equation is investigated by Homotopy perturbation method. Selection of a linear operator, which is a part of the main operator, is one of the main steps in HPM. If the aim is to obtain a periodic solution, this choice does not work here. To overcome this lack, a linear operator is imposed, and Fourier series of sines will be used in solving the linear equations arise in the HPM. Comparison of the results, with those of resulted by Differential Transformation and Harmonic Balance Method, shows an excellent agreement.     

Global dynamics of the periodic logistic system with periodic impulsive perturbations

This paper studies the global behaviors of the periodic logistic system with periodic impulsive perturbations. The results of D.D. Bainov and P.S. Simeonov (1993) are extended and dynamics different from the corresponding continuous system are found. It is shown that the system may have a unique positive periodic solution which is globally asymptotically stable, or go extinct when the two periods are rational dependent. When they are rational independent, the system has no periodic solutions, however, still has a global attractor or go extinct under some conditions.     

Permanence and extinction analysis for a delayed periodic predator-prey system with Holling type II response function and diffusion

In this paper, it is studied that two species predator-prey Lotka-Volterra type dispersal system with delay and Holling type II response function, in which the prey species can disperse among n patches, while the density-independent predator species is confined to one of the patches and cannot disperse. Sufficient conditions of integrable form for the boundedness, permanence, extinction and the existence of positive periodic solution are established, respectively.