32 Results Found

In this paper, a three-terminal memristor is constructed and studied through changing dual-port output instead of one-port. A new conservative memristor-based chaotic system is built by embedding this three-terminal memristor into a newly proposed fo...

In recent works by Wu and Wang a class of explicit symplectic integrators in curved spacetimes was presented. Different splitting forms or appropriate choices of time-transformed Hamiltonians are determined based on specific Hamiltonian problems. As...

We study the transition from integrability to chaos for the three-particle Fermi–Pasta–Ulam–Tsingou (FPUT) model. We can show that both the quartic $\beta$-FPUT model ($\alpha =0$) and the cubic one ($\beta =0$) are integrable by introdu...

We show that the most important measures of quantum chaos, such as frame potentials, scrambling, Loschmidt echo and out-of-time-order correlators (OTOCs), can be described by the unified framework of the isospectral twirling, namely the Haar average...

Many force–gradient explicit symplectic integration algorithms have been designed for the Hamiltonian $H=T\left(\mathbf{p}\right)+V\left(\mathbf{q}\right)$ with kinetic energy $T\left(\mathbf{p}\right)={\mathbf{p}}^2/2$ in the existing references. When a force–gradient operator is appropriately adjusted as a new operator, it...

In this study, the design of an adaptive terminal sliding mode controller for the stabilization of port Hamiltonian chaotic systems with hidden attractors is proposed. This study begins with the design methodology of a chaotic oscillator with a hidde...

In this paper, we study the different types of trajectories that correspond to a particular orbital behavior of caldera-type Hamiltonian systems. This particular orbital behavior is dynamical matching. Dynamical matching is an important chemical phen...

Recent progress towards understanding the mechanism of dynamical tunneling in Hamiltonian systems with three or more degrees of freedom (DoF) is reviewed. In contrast to systems with two degrees of freedom, the three or more degrees of freedom case p...

In this review work, we outline a conceptual path that, starting from the numerical investigation of the transition between weak chaos and strong chaos in Hamiltonian systems with many degrees of freedom, comes to highlight how, at the basis of equil...

In relativistic celestial mechanics, post-Newtonian (PN) Lagrangian and PN Hamiltonian formulations are not equivalent to the same PN order as our previous work in PRD (2015). Usually, an approximate Lagrangian is used to discuss the difference betwe...

The existence of chaos and the quest of dense orbits have been recently considered for dynamical systems given by multivalued linear operators. We consider the notions of topological transitivity, topologically mixing property, hypercyclicity, period...

We explore the concept of scaling invariance in a type of dynamical systems that undergo a transition from regularity to chaos. The systems are described by a two-dimensional, nonlinear mapping that preserves the area in the phase space. The key vari...

The Hamiltonian character of the ray tracing equations describing the propagation of the Lower Hybrid Wave (LHW) in a magnetic confined plasma device (tokamak) is investigated in order to study the evolution of the parallel wave number along the prop...

In the present paper, we study both classical and quantum Hénon–Heiles systems. In particular, we make a comparison between the classical and quantum trajectories of integrable and nonintegrable Hénon–Heiles Hamiltonians. Fr...

There are two free coupling parameters $c_{13}$ and $c_{14}$ in the Einstein–Æther metric describing a non-rotating black hole. This metric is the Reissner–Nordström black hole solution when $0\le 2c_{13}<c_{14}<2$...

The nonadditive entropy S_q has been introduced in 1988 focusing on a generalization of Boltzmann–Gibbs (BG) statistical mechanics. The aim was to cover a (possibly wide) class of systems among those very many which violate hypothesis such as ergodici...

We show the existence of complex dynamics for a seasonally perturbed version of the Goodwin growth cycle model, both in its original formulation and for a modified formulation, encompassing nonlinear expressions of the real wage bargaining function a...

In this paper, we study non-equilibrium dynamics induced by a sudden quench of strongly correlated Hamiltonians with all-to-all interactions. By relying on a Sachdev-Ye-Kitaev (SYK)-based quench protocol, we show that the time evolution of simple spi...

This study presents a qualitative analysis of the fractional coupled nonlinear Schrödinger equation (FCNSE) to obtain its complete set of solutions. An appropriate wave transformation is applied to reduce the FCNSE to a fourth-order dynamical sy...

Based on the scalar–tensor–vector modified gravitational theory, a modified gravity Schwarzschild black hole solution has been given in the existing literature. Such a black hole spacetime is obtained through the inclusion of a modified g...

Suppose that G is a graph over n vertices. G has n eigenvalues (of adjacency matrix) represented by ${\lambda }_1,{\lambda }_2,\cdots ,{\lambda }_n$. The Gaussian Estrada index, denoted by $H\left(G\right)$ (Estrada et al., Chaos 27(2017) 023109), can be defined as $H\left(G\right)={\sum }_{i=1}^n$...

The trans-Neptunian region (30–50 AU) is a dynamically structured reservoir of icy planetesimals whose orbital architecture reflects resonant dynamics, chaotic transport, and long-term gravitational sculpting by the giant planets. This review s...

We take into account the dynamics of three types of models of rotating galaxies in polar coordinates in a rotating frame. Due to non-axisymmetric potential perturbations, the angular momentum varies with time, and the kinetic energy depends on the mo...

Non-Hermitian optics has revealed a series of counterintuitive phenomena with profound implications for sensing, lasing, and light manipulation. While the non-Hermiticity of Hamiltonians has been intensively investigated, recent advancements in the n...

We study the planar repulsive two-center Coulomb system in the presence of a uniform magnetic field perpendicular to the plane, taking the inter-center separation a and the magnetic field strength B as independent control parameters. The free-field s...

This study investigates the dynamics of dust acoustic periodic waves in a three-component, unmagnetized dusty plasma system using generalized $(r^{\star },q^{\star })$ distributions. First, boundary conditions are applied to reduce the model to a second-or...

This study investigates the ($3+1$)-dimensional extended Kadomtsev–Petviashvili equation via traveling-wave phase-space geometry. The equation is reduced to a planar Hamiltonian system with cubic nonlinearity, whose conserved energy partitions th...

Quantum walks are, at present, an active field of study in mathematics, with important applications in quantum information and statistical physics. In this paper, we determine the influence of basic chaotic features on the walker behavior. For this p...

The purpose of this study is to construct diverse forms of exact soliton solutions and conduct a comprehensive qualitative analysis. For this aim, we use the Gross–Pitaevskii system, which belongs to the family of nonlinear Schrödinger equ...

In this paper, the nonlinear Nurshuak–Tolkunay–Myrkakulov (NTM-III) equation is analyzed using the methods of dynamical systems theory and exact solution techniques. The NTM-III model is reduced to a second-order nonlinear ordinary differ...

We introduce the Hamiltonian pseudorandom function (HPRF), a new symmetric cryptographic primitive in which the function family $\left\{F_k\right\}$ is defined by $F_k\left(q\right)=\nabla S_k\left(q\right)$, the gradient of the generating function of a secret Lagrangian submanifold $L_k$ on th...

In this work, we explore the nonlinear wave phenomena of the (3+1)-dimensional Boussinesq (II) equation, a significantly higher-dimensional model that describes dispersive wave propagation in fluid dynamics, plasma systems, and nonlinear optics. Usin...