Related papers: Hysteresis in Adiabatic Dynamical Systems: an Intr…
Hysteresis can be found in driven many-body systems such as magnets and superfluids. Rate-dependent hysteresis arises when a system is driven periodically while relaxing towards equilibrium. A two-state paramagnet driven by an oscillating…
In a standard bifurcation of a dynamical system, the stationary points (or more generally attractors) change qualitatively when varying a control parameter. Here we describe a novel unusual effect, when the change of a parameter, e.g. a…
Let the adiabatic invariant of action variable in slow-fast Hamiltonian system with two degrees of freedom have two limiting values along the trajectories as time tends to infinity. The difference of two limits is exponentially small in…
Describing dynamic medical systems using machine learning is a challenging topic with a wide range of applications. In this work, the possibility of modeling the blood glucose level of diabetic patients purely on the basis of measured data…
We study localisation transition in a class of quasi-periodic systems that has two competing periodic scales. We show that such class of systems show a re-entrant localisation transition where the energy scale of transition is set by the…
The presence of global conserved quantities in interacting systems generically leads to diffusive transport at late times. Here, we show that systems conserving the dipole moment of an associated global charge, or even higher moment…
The majority of dynamical studies in power systems focus on the high voltage transmission grids where models consider large generators interacting with crude aggregations of individual small loads. However, new phenomena have been observed…
Unconventional cycles provide a useful didactic resource to discuss the second law of thermodynamics applied to thermal motors and their efficiency. In most cases they involve a negative slope, linear process that presents an adiabatic…
The nonexponential relaxation ocurring in complex dynamics manifested in a wide variety of systems is analyzed through a simple model of diffusion in phase space. It is found that the inability of the system to find its equilibrium state in…
We simulate the dynamics of paramagnetic colloidal particles that are placed above a magnetic hexagonal pattern and exposed to an external field periodically changing its direction along a control loop. The conformation of three colloidal…
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…
We review the depinning and nonequilibrium phases of collectively interacting particle systems driven over random or periodic substrates. This type of system is relevant to vortices in type-II superconductors, sliding charge density waves,…
Motivated by a stochastic differential equation describing the dynamics of interfaces, we study the bifurcation behavior of a more general class of such equations. These equations are characterized by a 2-dimensional phase space (describing…
We study a discrete non-autonomous system whose autonomous counterpart (with the frozen bifurcation parameter) admits a saddle-node bifurcation, and in which the bifurcation parameter slowly changes in time and is characterized by a sweep…
In the present paper we describe the dynamics of the revised rigid body, the dynamics of the rigid body with distributed delays and the dynamics of the fractional rigid body. We analyze the stationary states for given values of the rigid…
In many complex systems a continuous input of energy over time can be suddenly relaxed in the form of avalanches. Conventional avalanche models disregard the possibility of internal dynamical effects in the inter-avalanche periods, and thus…
Many biological systems can sense periodical variations in a stimulus input and produce well-timed, anticipatory responses after the input is removed. Such systems show memory effects for retaining timing information in the stimulus and…
The present paper is concerned with a nonlinear partial differential control system subject to a state-dependent and nonconvex control constraint. This system models the dynamics of populations in the vegetation--prey--predator framework…
We present a comprehensive numerical study of the phase behavior and dynamics of a three-dimensional active dumbbell system with attractive interactions. We demonstrate that attraction is essential for the system to exhibit nontrivial…
Adiabatic processes in the quantum Ising model and the anisotropic Heisenberg model are discussed. The adiabatic processes are assumed to consist in the slow variation of the strength of the magnetic field that environs the spin-systems.…