Related papers: Renormalization Group Approach to Oscillator Synch…
In this paper the equation of forced Van der Pol generalized oscillator is examined with renormalization group method. A brief recall of the renormalization group technique is done. We have applied this method to the equation of forced Van…
We investigate renormalization group limit cycles within the similarity renormalization group (SRG) and discuss their signatures in the evolved interaction. A quantitative method to detect limit cycles in the interaction and to extract…
Functional renormalisation group approach is applied to a system of kaons with finite chemical potential. A set of approximate flow equations for the effective couplings is derived and solved. At high scale the system is found to be at the…
We employ an adaptation of a strong-disorder renormalization-group technique in order to analyze the ferro-paramagnetic quantum phase transition of Ising chains with aperiodic but deterministic couplings under the action of a transverse…
The renormalization group flow is presented for the two-dimensional sine-Gordon model within the framework of the functional renormalization group method by including the wave-function renormalization constant. The…
We present a collective coordinate approach to describe coupled phase oscillators. We apply the method to study synchronisation in a Kuramoto model. In our approach an N-dimensional Kuramoto model is reduced to an n-dimensional ordinary…
Effective potential for scalar $\lambda\phi^4$ theory is obtained using the exact renormalization group method which includes both the usual one-loop contribution as well as the dominant higher loop effects. Our numerical calculation…
We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By means of computer simulations we find the relation between the intrinsic dynamics of each member of the population and their mutual interaction that…
We studied the correlated quasi-one-dimensional systems by one-loop renormalization group techniques in weak coupling. In contrast to conventional g-ology approach, we formulate the theory in terms of bilinear currents and obtain all…
Renormalization group theory is a powerful and intriguing technique with a wide range of applications. One of the main successes of renormalization group theory is the description of continuous phase transitions and the development of…
Rigorous conditions for cluster synchronization of Kuramoto oscillators are presented. The method of averaging plays an important role in stability analysis, but the standard Lyapunov's second method is not applicable due to the lack of…
We consider the properties of vibrational dynamics on random networks, with random masses and spring constants. The localization properties of the eigenstates contrast greatly with the Laplacian case on these networks. We introduce several…
We investigate two recently proposed multivariate time series analysis techniques that aim at detecting phase synchronization clusters in spatially extended, nonstationary systems with regard to field applications. The starting point of…
Group synchronization asks to recover group elements from their pairwise measurements. It has found numerous applications across various scientific disciplines. In this work, we focus on orthogonal and permutation group synchronization…
The onset of synchronization in networks of networks is investigated. Specifically, we consider networks of interacting phase oscillators in which the set of oscillators is composed of several distinct populations. The oscillators in a…
Quantum Heisenberg spin chains with random couplings and spin sizes are studied using a real-space renormalization group technique. These systems belong to a new universality class of disordered quantum spin systems realized in {\it e.g.}…
We study the phase synchronization between collective rhythms of fully locked oscillator groups. For weakly interacting groups of two oscillators with global sinusoidal coupling, we analytically derive the collective phase coupling…
We study collective behavior of locally-coupled limit-cycle oscillators with scattered intrinsic frequencies on $d$-dimensional lattices. A linear analysis shows that the system should be always desynchronized up to $d=4$. On the other…
For a class of coupled limit cycle oscillators, we give a condition on a linear coupling operator that is necessary and sufficient for exponential stability of the synchronous solution. We show that with certain modifications our method of…
We have developed a very efficient numerical algorithm of the strong disorder renormalization group method to study the critical behaviour of the random transverse-field Ising model, which is a prototype of random quantum magnets. With this…