Cover of: Periodic solutions of nonlinear dynamical systems | Eduard Reithmeier

Periodic solutions of nonlinear dynamical systems

numerical computation, stability, bifurcation, and transition to chaos
  • 171 Pages
  • 3.42 MB
  • 1833 Downloads
  • English
by
Springer-Verlag , Berlin, New York
Differential equations, Nonlinear -- Numerical Solutions, Differentiable dynamical sy
StatementEduard Reithmeier.
SeriesLecture notes in mathematics ;, 1483, Lecture notes in mathematics (Springer-Verlag) ;, 1483.
Classifications
LC ClassificationsQA3 .L28 no. 1483, QA372 .L28 no. 1483
The Physical Object
Paginationvi, 171 p. :
ID Numbers
Open LibraryOL1551885M
ISBN 103540545123, 0387545123
LC Control Number91031739

Limit cycles or, more general, periodic solutions of nonlinear dynamical systems occur in many different fields of application. Although, there is extensive literature on periodic solutions, in particular on existence theorems, the connection to physical and.

Buy Periodic Solutions of Nonlinear Dynamical Systems: Numerical Computation, Stability, Bifurcation, and Transition to Chaos (Lecture Notes in Mathematics) on FREE SHIPPING on qualified ordersCited by: M.U.

Akhmetov, Periodic solutions of systems of differential equations with a non classical right-hand side containing a small parameter (russian), TIC: Collection: asymptotic solutions of non linear equations with small parameter. d, 11–Author: Marat Akhmet. In Hamiltonian systems, topics like Birkhoff normal forms and the Poincaré-Birkhoff theorem on periodic solutions have been added.

Download Periodic solutions of nonlinear dynamical systems FB2

There are now 6 appendices with new material on invariant manifolds, bifurcation of strongly nonlinear self-excited systems and normal forms of Hamiltonian systems. In this paper, analytical solutions of periodic motions in a 1-D nonlinear dynamical system are obtained through the generalized harmonic balance method with prescribed-computational accuracy.

From this method, the 1-D dynamical system is transformed to a nonlinear dynamical system of coefficients in the Fourier by: 2. In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input.

Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in. In this paper, the generalized harmonic balance method is presented for approximate, analytical solutions of Periodic solutions of nonlinear dynamical systems book motions in nonlinear dynamical systems.

The nonlinear damping, periodically forced, Duffing oscillator is studied as a sample problem. The approximate, analytical solution of period-1 periodic motion of such an oscillator is. For values of a slightly bigger than 3, empirical observations of the time sequences for this nonlinear dynamical system generated by using a hand calculator, a digital computer, or our “pencil computer” reveals that the long-time behavior approaches a periodic cycle of period 2, which alternates between two different values of x.

Because. Discrete & Continuous Dynamical Systems - A,39 (8): doi: /dcds [5] Shiwang Ma. Nontrivial periodic solutions for asymptotically linear hamiltonian systems at resonance. Dynamical systems theory is an area of mathematics used to describe the behavior of the complex dynamical systems, usually by employing differential equations or difference differential equations are employed, the theory is called continuous dynamical a physical point of view, continuous dynamical systems is a generalization of.

Conservative systems represent a large number of naturally occurring and artificially designed scientific and engineering systems. A key consideration in the theory and application of nonlinear conservative systems is the solution of the governing nonlinear ordinary differential equation.

This chapter surveys the recent approximate analytical schemes for the periodic solution of nonlinear. Periodic behaviour of nonlinear, second-order discrete dynamical systems Article (PDF Available) in Journal of Difference Equations and Applications 22(2).

Furthermore, the existence of anti-periodic solutions can be applied to help better describe the dynamical properties of nonlinear systems [49][50][51][52][53] [54] [55][56][57][58][59][60][61][ A dynamical system is a manifold M called the phase (or state) space endowed with a family of smooth evolution functions Φ t that for any element of t ∈ T, the time, map a point of the phase space back into the phase space.

The notion of smoothness changes with applications and the type of manifold. There are several choices for the set T is taken to be the reals, the dynamical. () Periodic solutions of dynamical systems with bounded potential. Journal of Differential Equations() Solutions with minimal period for Hamiltonian systems in a.

5 Periodic solutions 35 Books • Nonlinear Dynamics and Chaos, by Steven H. Strogatz, Perseus Books Group, here: this book is commonly referred to as the picture book of dynamical systems. Ralph Abraham is one of the masters. What is a dynamical system. 2 Examples of realistic dynamical systems Driven nonlinear pendulum Figure shows a pendulum of mass M subject to a torque (the rotational equivalent of a force) and to a gravitational force G.

You may think, for. Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be very simple, yet they produce completely unpredictable and divergent behavior.

Systems of nonlinear equations are. In this article, we present a new accurate iterative and asymptotic method to construct analytical periodic solutions for a strongly nonlinear system, even if it is not Z2-symmetric.

This method is applicable not only to a conservative system but also to a non-conservative system with a limit cycle response. Distinct from the general harmonic balance method, it depends on balancing a.

the existence of multiple periodic solutions of a kind of nonlinear dynamic system with feedback control. Finally, in Section 5, sufficient conditions are derived ensuring the existence of at least one periodic solution of a more general nonlinear dynamic system with feedback control on time scales.

We deal with nonlinear periodic differential systems depending on a small parameter. The unperturbed system has an invariant manifold of periodic solutions.

We provide sufficient conditions in order that some of the periodic orbits of this invariant manifold persist after the perturbation.

These conditions are not difficult to check, as we show in some applications. *Here blue chapters/sections about maps are referring to Wiggins's book Introduction to applied nonlinear dynamical systems and chaos. "Dynamical" dynamical systems Below is a list of programs (in matlab)/animations that help you understand the material better.

• mith & Introduction to Dynamical Systems [CUP]. Also very good and clear, covers a lot of ground. • aw An Introduction to Nonlinear Ordinary Differential Equations [CRC Press]. Very good on stability of periodic solutions.

Quite technical in parts. • Nonlinear Systems [CUP]. Limit cycles or, more general, periodic solutions of nonlinear dynamical systems occur in many different fields of application.

Description Periodic solutions of nonlinear dynamical systems FB2

Rating: (not yet rated) 0 with reviews - Be the first. The construction proceeds by iterating a KAM theorem about the existence of quasi-periodic solutions for some partial differential equations. As a result, we find for ‘almost all’ potentials V uncountably many almost-periodic solutions accumulating at the zero solution.

NONLINEAR DYNAMICAL SYSTEMS finite speeds of signal propagation cause f to depend also on values of x at times earlier than t. In spatially extended systems, each system variable is a continuous func- tion of spatial position as well as time and the equations of.

Where many of studies and researches [36–40] dedicates for treatment the autonomous and non-autonomous periodic systems and specially with the integral equations and differential equations and the linear and nonlinear differential and which is dealing in general shape with the problems about periodic solutions theory and the modern methods in.

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The analytical solutions of periodic flows and chaos in autonomous systems will be discussed first, and the analytical dynamics of non-autonomous nonlinear dynamical systems will be presented. The analytical solutions of periodic motions in free and periodically excited vibration systems will be presented.

In this chapter, we investigate the existence and classification of nonoscillatory solutions of two-dimensional (2D) nonlinear time-scale systems of first-order dynamic equations.

The method we follow is based on the sign of components of nonoscillatory solutions and the most well-known fixed point theorems. In this paper, we consider nonlinear density-dependent mortality Nicholson’s blowflies system involving patch structures and asymptotically almost periodic environments.

By developing an approach based on differential inequality techniques coupled with the Lyapunov function method, some criteria are demonstrated to guarantee the global attractivity of the addressed systems.

Periodic Solutions of Nonlinear Dynamical Systems Numerical Computation, Stability, Bifurcation, and Transition to Chaos is a great book.

This book is written by author Reithmeier, E., Dold, A., Eckmann, B. You can read the Periodic Solutions of Nonlinear Dynamical Systems Numerical Computation, Stability, Bifurcation, and Transition to Chaos book on our .periodic solutions which are close to those of the linear equations (1)–(2).

As a motivation for what follows, let me sketch a proof of the existence of periodic solutions of (3)–(4), which is somewhat dif-ferent from standard demonstrations. Any periodic solution must be of the form x1(t)= X n2Z einÚtˆx (5) 1(n); x2(t)= X n2Z einÚtˆx.

The existence of affine-periodic solutions for dynamic equations on time scales is studied. Mainly, via the topological degree theory, a general existence theorem is proved, which provides an effective method in the qualitative theory for nonlinear dynamic .