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The Duffing oscillator is a nonlinear extension of the ubiquitous harmonic oscillator and as such plays an outstanding role in science and technology. Experimentally, the system parameters are determined by a measurement of its response to…
In this paper, we investigate the quantum dynamics of underlying two one-dimensional quadratic Li'enard type nonlinear oscillators which are classified under the category of maximal (eight parameter) Lie point symmetry group (J. Math.…
We derive a new renormalization group to calculate a non-trivial critical exponent of the divergent correlation length which gives a universality classification of essential singularities in infinite-order phase transitions. This method…
A modified renormalization group equation for the inverse extrapolation length $c$ is derived by considering the phase shifts of order parameter fluctuations. The resulting non-linear equation is also derived using standard methods and some…
In the present work, we explore the case of a general PT-symmetric dimer in the context of two both linearly and nonlinearly coupled cubic oscillators. To obtain an analytical handle on the system, we first explore the rotating wave…
We prove the existence of nonlinear normal modes for general systems of two coupled nonlinear oscillators. Facilitating the comparison principle for ordinary differential equations it is shown that there exist exact solutions representing a…
We derive the renormalization group equations for a generic nonrenormalizable theory. We show that the equations allow one to derive the structure of the leading divergences at any loop order in terms of one-loop diagrams only. In chiral…
We propose a novel and systematic method for coarse-graining oscillator networks described by phase equations. Our coarse-graining method enables us to obtain the closed coarse-grained equations for a few effective eigenmodes, which is…
We extend the Hertz-Millis theory of quantum phase transitions in itinerant electron systems to phases with broken discrete symmetry. Using a set of coupled flow equations derived within the functional renormalization group framework, we…
For perturbed ordinally differential equations, a procedure of renormalization group method is proposed. To uniquely obtain renormalized solutions for given initial conditions, the procedure assumes that the extra integral constants yielded…
The rotationally-covariant renormalization group equations of motion for the density wave amplitudes in the phase field crystal model are shown to follow from a dynamical equation driven by an effective free energy density that we derive.…
We establish the functional Renormalization Group as an exploratory tool to investigate a possible phase transition between a pre-geometric discrete phase and a geometric continuum phase in quantum gravity. In this paper, based on the…
We study the universal critical behaviour near weakly first-order phase transitions for a three-dimensional model of two coupled scalar fields -- the cubic anisotropy model. Renormalization-group techniques are employed within the formalism…
In this paper we extend the Gaussian self-consistent method to permit study of the equilibrium and kinetics of conformational transitions for heteropolymers with any given primary sequence. The kinetic equations earlier derived by us are…
Analyzing synchronized nonlinear oscillators is one of the most important and attractive topics in nonlinear science. By understanding the interactions between the oscillators, we can figure out the synchronization process. A promising…
In this paper, the problem of partial stabilization of nonlinear systems along a given trajectory is considered. This problem is treated within the framework of stability of a family of sets. Sufficient conditions for the asymptotic…
We derive the Wilsonian renormalization group equation in two dimensional ${\cal N}=2$ supersymmetric nonlinear sigma models. This equation shows that the sigma models on compact Einstein K\"{a}hler manifolds are aymptotically free. This…
To gain a deeper understanding of the glassy phase in $p$-spin quantum models, this paper examines the dynamics of the $N$-vector $\bm{x} \in \mathbb{R}^N$ through the framework of renormalization group theory. First, we focus on…
In this paper we introduce a diagrammatic equation for the planar sector of square non hermitian random matrix models strongly reminiscent of Polchinski's equation in quantum field theory. Our fundamental equation is first obtained by a…
New qualitative picture of vortex length-scale dependence has been found in recent electrical transport measurements performed on strongly anisotropic BSCCO single crystals in zero magnetic field. This indicates the need for a better…