Ratchet Transport and Periodic Structures in Parameter Space

Abstract

This work analyzes the parameter space of a discrete ratchet model and gives direct connections between chaotic domains and a family of isoperiodic stable structures with the ratchet current. The isoperiodic structures, where larger currents are usually observed inside, appear along preferred direction in the parameter space giving a guide to follow the current. Currents in parameter space provide a direct measure of the momentum asymmetry of the multistable and chaotic attractors times the size of the corresponding basin of attraction. Transport structures are shown to exist in the parameter space of the Langevin equation with an external oscillating force.

Quantum-classical transition and quantum activation of ratchet currents in the parameter space

“…Along the diagonal dark-green line (below the ISS B 1 ) where large activations (∆ ∼ 6) occur in Fig. 3(c), we conclude from classical results [13] that the activation is due to a crisis bifurcation. Additional numerical results revealed that the activation close to K = 2.5 and γ = 0.85 is related to a symmetry breaking of the multistable attractors.…”

“…The quantum-classical transition was studied by means of a comparison between the C S and C C . We show how and to which extent the classical generic isoperiodic stable structures [13,14,20] are destroyed by quantum fluctuations. Even though these structures become blurred and start to disappear in the quantum world, their sharp borders tend to persist when the correlation between quantum and classical currents is investigated.…”

“…Second, the four ISSs, B 1 , B 2 , C −1 and F . Besides F , which has zero current, the ISSs are responsible for the optimal C C and can be recognized by their sharp borders (for a detailed explanation see [13,14]). We note that at the crossing regions of B 1 and F , positive currents are observed as a consequence of multistable attractors.…”

“…It is known [10] that in classical conservative systems the parameters must be chosen so that the underlying dynamics presents a mixture of regular and chaotic motion. In dissipative inertial systems the Classical Ratchet Current (CRC) is more efficient when parameters are chosen inside the Isoperiodic Stable Structures (ISSs), which appear in the parameter space of ratchet models [13,14]. Such ISSs are generic Lyapunov stable islands with dynamics globally structurally stable and come along in many dynamical systems [15][16][17][18][19].…”

Characterizing the dynamics of three FitzHugh-Nagumo neurons network

“…The colors codify some measure that can be computed on the model. Usually, this measure is the Lyapunov exponent [1,3,7,9,13,14], periods [7,14], or other invariant measure [3]. This procedure allows us to identify regions of periodic, chaotic, and hyperchaotic behavior, and recently it is applied in several models.…”