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Consider a periodically forced nonlinear system which can be presented as a collection of smaller subsystems with pairwise interactions between them. Each subsystem is assumed to be a massive point moving with friction on a compact surface,…

Non-equilibrium dynamics are present in many aspects of our lives, ranging from microscopic physical systems to the functioning of the brain. What characterizes stochastic models of non-equilibrium processes is the breaking of the…

We simplify the proof of some widely used theoretical theorems, extending their applicability, while correcting some erroneous results. We also generalize key results and present new results that contribute to the development of the theory.…

This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…

Topology of levels of the quasiperiodic functions with m=n+2 periods on the plane is studied. For the case of functions with m=4 periods full description is obtained for the open everywhere dense family of functions. This problem is…

We investigate the effects of dichotomous noise added to a classical harmonic oscillator in the form of stochastic time-dependent gain and loss states, whose durations are sampled from two distinct exponential waiting time distributions.…

A nonlinear cyclic system with delay and the overall negative feedback is considered. The characteristic equation of the linearized system is studied in detail. Sufficient conditions for the oscillation of all solutions and for the…

Synchronization of coupled harmonic oscillators is investigated. Coupling considered here is pairwise, unidirectional, and described by a nonlinear function (whose graph resides in the first and third quadrants) of some projection of the…

In this paper we present a study of the non-linear effects of anharmonicity of the potential of the simple pendulum. In a theoretical reminder we highlight that anharmonicity of the potential generates additional harmonics and the…

The approach to equilibrium for systems interacting with their environment by being regularly exposed to low energy, low intensity pulses of some type of quanta is studied. Assuming a randomness condition on the interaction of these quanta…

In phase space, we analytically obtain the characteristic functions (CFs) of a forced harmonic oscillator [Talkner et al., Phys. Rev. E, 75, 050102 (2007)], a time-dependent mass and frequency harmonic oscillator [Deffner and Lutz, Phys.…

We study stochastic particle systems that conserve the particle density and exhibit a condensation transition due to particle interactions. We restrict our analysis to spatially homogeneous systems on finite lattices with stationary product…

An approach is presented for coupled chaotic systems, estimating an inferior bound value for the absolute phase difference, in order to say that phase synchronization is present. This approach shows that synchronicity in phase implies…

The existence of bi-Hamiltonian structures for the rational Harmonic Oscillator (non-central harmonic oscillator with rational ratio of frequencies) is analyzed by making use of the geometric theory of symmetries. We prove that these…

In this paper, we prove the boundary partial regularity for a class of coupled Dirac-harmonic maps satisfying a certain energy monotonicity inequality near the boundary.

We show the existence of homoclinic type solutions of second order Hamiltonian systems with a potential satisfying a relaxed superquadratic growth condition and a forcing term that is sufficiently small in the space of square integrable…

Generally, natural scientific problems are so complicated that one has to establish some effective perturbation or nonperturbation theories with respect to some associated ideal models. In this Letter, a new theory that combines…

Classical Hamiltonian systems with balanced loss and gain are considered in this review. A generic Hamiltonian formulation for systems with space-dependent balanced loss and gain is discussed. It is shown that the loss-gain terms may be…

In this paper, we introduce some new notions of aging based on geometric, harmonic means of failure rate and aging intensity function. We define a generalized version of aging functions called specific interval-average geometric hazard…

Motivated by recent problems in mathematical cosmology, in which temporal averaging methods are applied in order to analyze the future asymptotics of models which exhibit oscillatory behavior, we provide a theorem concerning the large-time…