Standard map
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Lyapunov Exponent and Out-of-Time-Ordered Correlator’s Growth Rate in a Chaotic System Open
It was proposed recently that the out-of-time-ordered four-point correlator (OTOC) may serve as a useful characteristic of quantum-chaotic behavior, because, in the semiclassical limit ℏ→0, its rate of exponential growth resembles the clas…
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A Robust and Fast Image Encryption Scheme Based on a Mixing Technique Open
This paper introduces a new image encryption scheme using a mixing technique as a way to encrypt one or multiple images of different types and sizes. The mixing model follows a nonlinear mathematical expression based on Cramer’s rule. Two …
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A Novel Audio Cryptosystem Using Chaotic Maps and DNA Encoding Open
Chaotic maps have good potential in security applications due to their inherent characteristics relevant to cryptography. This paper introduces a new audio cryptosystem based on chaotic maps, hybrid chaotic shift transform (HCST), and deox…
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Lyapunov exponents for random perturbations of some area-preserving maps including the standard map Open
We consider a large class of 2D area-preserving diffeomorphisms that are not\nuniformly hyperbolic but have strong hyperbolicity properties on large regions\nof their phase spaces. A prime example is the Standard map. Lower bounds for\nLya…
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A Posteriori Verification of Invariant Objects of Evolution Equations: Periodic Orbits in the Kuramoto--Sivashinsky PDE Open
In this paper, a method for computing periodic orbits of the Kuramoto--Sivashinsky PDE via rigorous numerics is presented. This is an application and an implementation of the theoretical method introduced in [J.-L. Figueras, M. Gameiro, J.…
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An Image Encryption Algorithm Based on Bisection Method and One-Dimensional Piecewise Chaotic Map Open
In this article, an image encryption algorithm via bisection method and one-dimensional piecewise chaotic map is proposed. It depends on the permutation-substitution model. Firstly, the pseudo-random sequence is defined using polynomial va…
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Characterizing weak chaos using time series of Lyapunov exponents Open
We investigate chaos in mixed-phase-space Hamiltonian systems using time series of the finite-time Lyapunov exponents. The methodology we propose uses the number of Lyapunov exponents close to zero to define regimes of ordered (stickiness)…
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Measuring quasiperiodicity Open
The Birkhoff Ergodic Theorem asserts under mild conditions that Birkhoff averages (i.e. time averages computed along a trajectory) converge to the space average. For sufficiently smooth systems, our small modification of numerical Birkhoff…
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Global and local diffusion in the standard map Open
We study the global and the local transport and diffusion in the case of the standard map, by calculating the diffusion exponent μ. In the global case, we find that the mean diffusion exponent for the whole phase space is either μ=1, denot…
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Resonance Eigenfunction Hypothesis for Chaotic Systems Open
A hypothesis about the average phase-space distribution of resonance eigenfunctions in chaotic systems with escape through an opening is proposed. Eigenfunctions with decay rate γ are described by a classical measure that (i) is conditiona…
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Chaotic Path Planner of Autonomous Mobile Robots Based on the Standard Map for Surveillance Missions Open
This paper proposes a fusion iterations strategy based on the Standard map to generate a chaotic path planner of the mobile robot for surveillance missions. The distances of the chaotic trajectories between the adjacent iteration points wh…
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An improvement on the chaotic behavior of the Gauss Map for cryptography purposes using the Circle Map combination Open
Chaos based cryptography has becoming an interesting topic lately, as it utilizes chaotic systems properties for secure key concealment. Many chaotic functions are discovered, constructed, and used time over time for this purpose, which wi…
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Perturbation-free prediction of resonance-assisted tunneling in mixed regular-chaotic systems Open
For generic Hamiltonian systems we derive predictions for dynamical tunneling from regular to chaotic phase-space regions. In contrast to previous approaches, we account for the resonance-assisted enhancement of regular-to-chaotic tunnelin…
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On the origin of chaotic attractors with two zero Lyapunov exponents in a system of five biharmonically coupled phase oscillators Open
We study chaotic dynamics in a system of four differential equations describing the interaction of five identical phase oscillators coupled via biharmonic function. We show that this system exhibits strange spiral attractors (Shilnikov att…
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Statistical and dynamical properties of the quantum triangle map Open
We study the statistical and dynamical properties of the quantum triangle map, whose classical counterpart can exhibit ergodic and mixing dynamics, but is never chaotic. Numerical results show that ergodicity is a sufficient condition for …
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Chaos-Based Image Encryption Using Arnold’s Cat Map Confusion and Henon Map Diffusion Open
\nThis research designed an image encryption system that focused on securing teledermatology data in the form of skin disease images. The encryption and decryption process of this system is done on the client side using chaos-based encrypt…
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Theory of short periodic orbits for partially open quantum maps Open
We extend the semiclassical theory of short periodic orbits [M. Novaes et al., Phys. Rev. E 80, 035202(R) (2009)PLEEE81539-375510.1103/PhysRevE.80.035202] to partially open quantum maps, which correspond to classical maps where the traject…
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Disentangling regular and chaotic motion in the standard map using complex network analysis of recurrences in phase space Open
Recurrence in the phase space of complex systems is a well-studied phenomenon, which has provided deep insights into the nonlinear dynamics of such systems. For dissipative systems, characteristics based on recurrence plots have recently a…
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Characteristic times in the standard map Open
We study and compare three characteristic times of the standard map: the Lyapunov time t_{L}, the Poincaré recurrence time t_{r}, and the stickiness (or escape) time t_{st}. The Lyapunov time is the inverse of the Lyapunov characteristic n…
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Stickiness in generic low-dimensional Hamiltonian systems: A recurrence-time statistics approach Open
We analyze the structure and stickiness in the chaotic components of generic Hamiltonian systems with divided phase space. Following the method proposed recently in Lozej and Robnik [Phys. Rev. E 98, 022220 (2018)2470-004510.1103/PhysRevE.…
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Fingerprint of chaos and quantum scars in kicked Dicke model: an out-of-time-order correlator study Open
We investigate the onset of chaos in a periodically kicked Dicke model (KDM), using the out-of-time-order correlator (OTOC) as a diagnostic tool, in both the oscillator and the spin subspaces. In the large spin limit, the classical Hamilto…
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Complex-path prediction of resonance-assisted tunneling in mixed systems Open
We present a semiclassical prediction of regular-to-chaotic tunneling in systems with a mixed phase space, including the effect of a nonlinear resonance chain. We identify complex paths for direct and resonance-assisted tunneling in the ph…
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Recurrence-time statistics in non-Hamiltonian volume-preserving maps and flows Open
We analyze the recurrence-time statistics (RTS) in three-dimensional non-Hamiltonian volume-preserving systems (VPS): an extended standard map and a fluid model. The extended map is a standard map weakly coupled to an extra dimension which…
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Performance of chaos diagnostics based on Lagrangian descriptors. Application to the 4D standard map Open
We investigate the ability of simple diagnostics based on Lagrangian descriptor (LD) computations of initially nearby orbits to detect chaos in conservative dynamical systems with phase space dimensionality higher than two. In particular, …
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A generalization of the standard map and its statistical characterization Open
From the statistical mechanical point of view, area-preserving maps have great potential and importance. These maps exhibit chaotic and regular behavior separately or together in the available phase space as the control parameter changes. …
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Recurrence-based analysis of barrier breakup in the standard nontwist map Open
We study the standard nontwist map that describes the dynamic behaviour of magnetic field lines near a local minimum or maximum of frequency. The standard nontwist map has a shearless invariant curve that acts like a barrier in phase space…
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Chaotic and fractal maps in higher-order derivative dynamical systems Open
Hamiltonian maps are considered a class of dynamical systems that hold meticulous properties used to model a large number of complex dynamical systems. When time flows in dynamical systems with two-dimensional degrees of freedom, the traje…
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Periodic Orbits of the Logistic Map in Single and Double Precision Implementations Open
In finite precision implementations of chaotic maps all trajectories are eventually periodic. The goal of this brief is to develop methods for systematic study of effects of finite precision computations on dynamical behaviors of discrete …
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Extensive Numerical Results for Integrable Case of Standard Map Open
In recent years, conservative dynamical systems have become a vivid area of research from the statistical mechanical characterization viewpoint. With this respect, several areapreserving maps have been studied. It has been numerically show…
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Chaos-assisted tunneling in the presence of Anderson localization Open
Tunneling between two classically disconnected regular regions can be strongly affected by the presence of a chaotic sea in between. This phenomenon, known as chaos-assisted tunneling, gives rise to large fluctuations of the tunneling rate…