Related papers: When an oscillating center in an open system under…
We have presented an unified scheme to express a class of system of equations in two variables into a Li\'enard-Levinson-Smith (LLS) oscillator form. We have derived the condition for limit cycle with special reference to Rayleigh and…
We have examined a class of Li\'enard--Levinson--Smith (LLS) system having a stable limit cycle which demonstrates the case where the LLS theorem cannot be applied. The problem has been partly raised in a recent communication by Saha et…
In dynamical systems theory, there is a lack of a straightforward rule to distinguish exact center solutions from decaying center-like solutions, as both require the damping force function to be zero [1, 2]. By adopting a multi-scale…
Van der Pol and Rayleigh oscillators are two traditional paradigms of nonlinear dynamics. They can be subsumed into a general form of Li\'enard--Levinson--Smith(LLS) system. Based on a recipe for finding out maximum number of limit cycles…
Numerical evidence is given that spherically symmetric perturbations of stable spherically symmetric steady states of the gravitational Vlasov-Poisson system lead to solutions which oscillate in time. The oscillations can be periodic in…
Chemical oscillation is an interesting nonlinear dynamical phenomenon which arises due to complex stability condition of the steady state of a reaction far away from equilibrium which is usually characterised by a periodic attractor or a…
In this paper we indicate a general method to calculate the power law that governs how electronic LDOS oscillations decay far away from a surface step edge (or any local linear barrier), in the energy range when only 2D surface states are…
We study synchronization in a system of phase-only oscillators residing on the sites of a one-dimensional periodic lattice. The oscillators interact with a strength that decays as a power law of the separation along the lattice length and…
We study the dynamics of the SK model modified by a small non-hamiltonian perturbation. We study aging, and we find that on the time scales investigated by our numerical simulations it survives a small perturbation (and is destroyed by a…
In this paper a generalized Rayleigh-Li\'enard oscillator is consider and lower bounds for the number of limit cycles bifurcating from weak focus equilibria and saddle connections are provided. By assuming some open conditions on the…
We determine the late-time dynamics of a generic spin ensemble with inhomogeneous broadening - equivalently, qubits with arbitrary Zeeman splittings - coupled to a dissipative environment with strength decreasing as $1/t$. The approach to…
We compute the cyclicity of open period annuli of the following generalized Rayleigh-Li\'enard equation $$\ddot{x}+ax+bx^3-(\lambda_1+\lambda_2 x^2+\lambda_3\dot{x}^2+\lambda_4 x^4+\lambda_5\dot{x}^4+\lambda_6 x^6)\dot{x}=0$$ and the…
Orientational dynamics in a liquid crystalline system near the isotropic-nematic (I-N) phase transition is studied using Molecular Dynamics simulations of the well-known Lebwohl-Lasher (LL) model. As the I-N transition temperature is…
A theoretical analysis [Angelani et al., Phys. Rev. Lett. 96, 065702 (2006)] predicts glassy behaviour of light in a nonlinear random medium. This implies slow dynamics related to the presence of many metastable states. We consider very…
Geometric singular perturbation theory provides a powerful mathematical framework for the analysis of 'stationary' multiple time-scale systems which possess a critical manifold, i.e. a smooth manifold of steady states for the limiting fast…
Considering Limit Cycles as one of the limits of Lienard equation, an analyis analogous to centre manifold analysis has been done for a $3-D$ nonlinear system exhibiting Limit Cycle. A rigorous study on radius of the Limit Cycle orbit has…
Decay laws of moving unstable quantum systems with oscillating decay rates are analyzed over intermediate times. The transformations of the decay laws at rest and of the intermediate times at rest, which are induced by the change of…
We study the linearized Vlasov-Poisson equation in the gravitational case around steady states that are decreasing and continuous functions of the energy. We identify the absolutely continuous spectrum and give criteria for the existence of…
We study the dynamics of the Lipkin-Meshkov-Glick (LMG) model with finite number of spins. In the thermodynamic limit, the ground state of the LMG model with isotropic Hamiltonian in broken phase breaks to a mean-field ground state with a…
We theoretically study the power-law decay behavior of the local density of states (LDOS) oscillations near a line defect in system with semi-Dirac points by using a low-energy k.p Hamiltonian. We find that the LDOS oscillations are…