Related papers: Limit Cycle Analysis of 3-D Nonlinear systems

The Central Limit Theorem for Iterated Functions Systems on the circle is proved. We study also ergodicity of such systems.

Periodic normal forms for the codim 2 bifurcations of limit cycles up to a 3-dimensional center manifold in generic autonomous ODEs and computational formulas for their coefficients are derived. The formulas are independent of the dimension…

This paper studies bifurcations in a three node power system when excitation limits are considered. This is done by approximating the limiter by a smooth function to facilitate bifurcation analysis. Spectacular qualitative changes in the…

The averaging theory has been extensively employed for studying periodic solutions of smooth and nonsmooth differential systems. Here, we extend the averaging theory for studying periodic solutions a class of regularly perturbed…

The Kozai-Lidov mechanism can be applied to a vast variety of astrophysical systems involving hierarchical three-body systems. Here, we study the Kozai-Lidov mechanism systematically in the test particle limit at the octupole level of…

Inspired by the observation of a distributed time delay in the nonlinear response of an optical resonator, we investigate the effects of a similar delay on a noise-driven mechanical oscillator. For a delay time that is commensurate with the…

For the study of highly nonlinear, conservative dynamic systems, finding special periodic solutions which can be seen as generalization of the well-known normal modes of linear systems is very attractive. However, the study of…

It this paper we study a class of perturbed Hamiltonian systems under perturbations of thirteen order in order to detect the number of limit cycles which bifurcate from some periodic orbits of the unperturbed Hamiltonian system. The system…

We present an algorithm for the following problem. Given a triangulated 3-manifold M and a (possibly non-simple) closed curve on the boundary of M, decide whether this curve is contractible in M. Our algorithm runs in space polynomial in…

The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…

In this paper, we study the problem of limit cycle bifurcation in two piecewise polynomial systems of Li\'enard type with multiple parameters. Based on the developed Melnikov function theory, we obtain the maximum number of limit cycles of…

We derive sufficient conditions for the solvability of the state estimation problem for a class of nonlinear control time-varying systems which includes those, whose dynamics have triangular structure. The state estimation is exhibited by…

We study the orbital evolution of a three planet system with masses in the super-Earth regime resulting from the action of tides on the planets induced by the central star which cause orbital circularization. We consider systems either in…

Conditional dynamics due to continuous optical measurements has successfully been applied for state reconstruction and feedback cooling in optomechanical systems. In this article, we show that the same measurement techniques can be used to…

Bilinear systems emerge in a wide variety of fields as natural models for dynamical systems ranging from robotics to quantum dots. Analyzing controllability of such systems is of fundamental and practical importance, for example, for the…

The aim of this paper is to study global bifurcations of non-constant solutions of some nonlinear elliptic systems, namely the system on a sphere and the Neumann problem on a ball. We study the bifurcation phenomenon from families of…

This paper introduces an algorithmic approach to the analysis of bifurcation of limit cycles from the centers of nonlinear continuous differential systems via the averaging method. We develop three algorithms to implement the averaging…

By introducing a max-plus dynamical system having limit cycles, we discuss their periodicity, especially the number of discrete states in them. We also find that quasi-periodic cycles exist depending on the bifurcation parameter in the…

The goal of this paper is to study the number of sliding limit cycles of a regularized piecewise linear $VI_3$ two-fold using the notion of slow divergence integral. We focus on limit cycles produced by canard cycles located in the…

The class of 2-dimensional non-integrable flat dynamical systems has a rather extensive literature with many deep results, but the methods developed for this type of problems, both the traditional approach via Teichm\"{u}ller geometry and…