Related papers: Quantum Entanglement and fixed point Hopf bifurcat…
We consider a model proposed by one of the authors for a type of plastic instability found in creep experiments which reproduces a number of experimentally observed features. The model consists of three coupled non-linear differential…
Nonresonant Hopf-Hopf singularity in neutral functional differential equation (NFDE) is considered. An algorithm for calculating the third-order normal form is established by using the formal adjoint theory, center manifold theorem and the…
How does the classical phase space structure for a composite system relate to the entanglement characteristics of the corresponding quantum system? We demonstrate how the entanglement in nonlinear bipartite systems can be associated with a…
This is a preliminary study for bifurcation in fractional order dynamical systems. Stability, persistence and hopf bifurcation are studied. Some studies are also done for functional equations.
The present paper addresses the swing equation with additional delayed damping as an example for pendulum-like systems. In this context, it is proved that recurring sub- and supercritical Hopf bifurcations occur if time delay is increased.…
An exactly solvable Kitaev model in a two-dimensional square lattice exhibits a topological quantum phase transition which is different from the symmetry-breaking transition at zero temperature. When the ground state of a nonlinearly…
We present a bifurcation analysis of a normal form for travelling waves in one-dimensional excitable media. The normal form which has been recently proposed on phenomenological grounds is given in form of a differential delay equation. The…
Topological quantum phase transitions are characterised by changes in global topological invariants. These invariants classify many body systems beyond the conventional paradigm of local order parameters describing spontaneous symmetry…
Systems of ODEs coupled with the topology of a closed ring are common models in biology, robotics, electrical engineering, and many other areas of science. When the component systems and couplings are identical, the system has a cyclic…
We consider two different collective spin systems subjected to strong dissipation -- on the same scale as interaction strengths and external fields -- and show that either continuous or discontinuous dissipative quantum phase transitions…
We consider the Dicke Hamiltonian, a simple quantum-optical model which exhibits a zero-temperature quantum phase transition. We present numerical results demonstrating that at this transition the system changes from being quasi-integrable…
We investigate a diffusive, stage-structured epidemic model with the maturation delay and freely-moving delay. Choosing delays and diffusive rates as bifurcation parameters, the only possible way to destabilize the endemic equilibrium is…
In order to investigate the quantum phase transition in the one-dimensional quantum compass model, we numerically calculate non-local string correlations, entanglement entropy, and fidelity per lattice site by using the infinite matrix…
We study a model describing $N$ identical bosonic atoms trapped in a double-well potential together with a single impurity atom, comparing and contrasting it throughout with the Dicke model. As the boson-impurity coupling strength is…
We propose a new simple three-dimensional continuous autonomous model with two nonlinear terms and observe the dynamical behavior with respect to system parameters. This system changes the stability of fixed point via Hopf bifurcation and…
We report a new oscillatory form in the two coupled dissipative Rydberg atomic chains by modulating its spacing. Such oscillation has $\pi$-phase difference between two neighboring sites, which distinguishes itself from…
We consider the "membrane in the middle" optomechanical model consisting of a laser pumped cavity which is divided in two by a flexible membrane that is partially transmissive to light and subject to radiation pressure. Steady state…
Strongly correlated materials often undergo a Mott metal-insulator transition, which is tipically first-order, as a function of control parameters like pressure. Upon doping, rich phase diagrams with competing instabilities are found. Yet,…
We study a quantum phase transition between a phase which is topologically ordered and one which is not. We focus on a spin model, an extension of the toric code, for which we obtain the exact ground state for all values of the coupling…
We investigate the quantum phase transitions of the extended Hubbard model at half-filling with periodic boundary conditions employing the entanglement of particles, as opposed to the more traditional entanglement of modes. Our results show…