Related papers: Controllability near a homoclinic bifurcation
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
we consider a system with homoclinic orbit, We decompose the corresponding variational equation on the space of solutions and provide sufficient conditions for the permanency of homoclinic in the space of $C^1$ vector fields. We also…
Our ability to control complex systems is a fundamental challenge of contemporary science. Recently introduced tools to identify the driver nodes, nodes through which we can achieve full control, predict the existence of multiple control…
We discuss control of low-dimensional systems which, when uncontrolled, are integrable in the Hamiltonian sense. The controller targets an exact solution of the system in a region where the uncontrolled dynamics has invariant tori. Both…
The influence of disordering upon critical behavior of the system with hidden degrees of freedom is considered. It is shown that there is a tricritical behavior in the constrained system, while in the unconstrained system only phase…
An exact and analytic control protocol of two types of finite dimensional quantum systems is proposed. The system can be drive to an arbitrary target state using cosine classical fields in finite cycles. The control parameters which are…
In quantum control theory, the fundamental issue of controllability covers the questions whether and under which conditions a system can be steered from one pure state into another by suitably tuned time evolution operators. Even though Lie…
We construct general models for holographic superconductivity parametrized by three couplings which are functions of a real scalar field and show that under general assumptions they describe superconducting phase transitions. While some…
We study a two-dimensional Kolmogorov system when its two parameters vary in a small neighbourhood of the value $0.$ The local behavior of the system is described in terms of bifurcation diagrams.
We study homoclinic bifurcations in an interval map associated with a saddle-focus of (2, 1)-type in $\mathbb{Z}_2$-symmetric systems. Our study of this map reveals the homoclinic structure of the saddle-focus, with a bifurcation unfolding…
We propose to determine the bifurcation diagrams of fixed points using their coordinates as control parameters. This method can lead to exact solutions to otherwise intractable bifurcation problems.
The paper addresses an existence problem for infinite horizon optimal control when the system under control is exponentially stabilizable or stable. Classes of nonlinear control systems for which infinite horizon optimal controls exist are…
A boundary equilibrium bifurcation (BEB) in a hybrid dynamical system occurs when a regular equilibrium collides with a switching surface in phase space. This causes a transition to a pseudo-equilibrium embedded within the switching…
In this paper, we define four different notions of controllability of physical interest for multilevel quantum mechanical systems. These notions involve the possibility of driving the evolution operator as well as the state of the system.…
In this paper, we consider a hierarchical control problem with model uncertainty. Specifically, we consider the following objectives that we would like to accomplish. The first one being of a controllability-type that consists of…
Nonlinear dynamical systems, ranging from insect populations to lasers and chemical reactions, might exhibit sensitivity to small perturbations in their control parameters, resulting in uncertainties on the predictability of tunning…
In a network of spin 1/2 particles, controlled through an external electro-magnetic field, the gyromagnetic ratio of each spin is a parameter that characterizes the interaction of the spin with the external control field. Multipartite…
Controllability -- the possibility of performing any target dynamics by applying a set of available operations -- is a fundamental requirement for the practical use of any physical system. For finite-dimensional systems, as for instance…
The dynamical systems of planet-belt interaction are studied by the fixed-point analysis and the bifurcation of solutions on the parameter space is discussed. For most cases, our analytical and numerical results show that the locations of…
Stable and unstable manifolds, originating from hyperbolic cycles, fundamentally characterize the behaviour of dynamical systems in chaotic regions. This letter demonstrates that their shifts under perturbation, crucial for chaos control,…