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Concepts from the field of wave chaos have been shown to successfully predict the statistical properties of linear electromagnetic fields in electrically large enclosures. The Random Coupling Model (RCM) describes these properties by…
Dynamic perturbation equations are derived for a generic stationary state of an elastic string model -- of the kind appropriate for representing a superconducting cosmic string -- in a flat background. In the case of a circular equilibrium…
Nonlinear isolated and coupled oscillators are extensively studied as prototypical nonlinear dynamics models. Much attention has been devoted to oscillator synchronization or the lack thereof. Here, we study the synchronization and…
Here we numerically study a model of excitable media, namely, a network with occasionally quiet nodes and connection weights that vary with activity on a short-time scale. Even in the absence of stimuli, this exhibits unstable dynamics,…
The motion of oscillatory-like nonlinear Hamiltonian systems, driven by a weak noise, is considered. A general method to find regions of stability in the phase space of a randomly-driven system, based on a specific Poincar\'e map, is…
We use physical principles to derive a water wheel model under the assumption of an asymmetric water wheel for which the water inflow rate is in general unsteady (modeled by an arbitrary function of time). Our model allows one to recover…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…
Small-sized systems exhibit a finite number of routes to chaos. However, in extended systems, not all routes to complex spatiotemporal behavior have been fully explored. Starting from the sine-Gordon model of parametrically driven chain of…
We study synchronization dynamics in populations of coupled phase oscillators with higher-order interactions and community structure. We find that the combination of these two properties gives rise to a number of states unsupported by…
A possibility of a nonlinear resonant instability of uniform oscillations in dynamical lattices with harmonic intersite coupling and onsite nonlinearity is predicted. Numerical simulations of a lattice with a double-well onsite anharmonic…
We study the plane (not necessarily monochromatic) gravitational waves at nonlinear quadratic order on a flat background in vacuum. We show that, in the harmonic gauge, the nonlinear waves are unstable. We argue that, at this order, this…
For a one-dimensional motion, a constant of motion for non autonomous an linear system (position and velocity) is given from the constant of motion associated to its autonomous system. This approach is used in the study of the harmonic…
We study synchronization of nonlinear systems that satisfy an incremental passivity property. We consider the case where the control input is subject to a class of disturbances, including constant and sinusoidal disturbances with unknown…
The harmonic oscillator is an essential tool, widely used in all branches of Physics in order to understand more realistic systems, from classical to quantum and relativistic regimes. We know that the harmonic oscillator is integrable in…
Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological…
Forced oscillation (FO) is a significant concern threating the power system stability. Its mechanisms are mostly studied via linear models. However, FO amplitude is increasing, e.g., Nordic and Western American FOs, which can stimulate…
Non-linear dynamics is not a usually covered topic in undergraduate physics courses. However, its importance within classical mechanics and the general theory of dynamical systems is unquestionable. In this work we show that this subject…
Modulation instability in a nonlinear optical waveguide array with alternating positive and negative refractive indices is investigated analytically. Particular solutions of a system of coupled nonlinear equations are found. These solutions…
A solvable model of noise effects on globally coupled limit cycle oscillators is proposed. The oscillators are under the influence of independent and additive white Gaussian noise. The averaged motion equation of the system with infinitely…
A study of the non linear modes of a two degree of freedom mechanical system with bilateral elastic stop is considered. The issue related to the non-smoothness of the impact force is handled through a regularization technique. In order to…