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The average shape of the Spectral Local Density of States (LDOS) and eigenfunctions (EFs) has been studied numerically for a conservative dynamical model (three-orbital Lipkin-Meshkov-Glick model) which can exhibit strong chaos in the classical limit. The attention is paid to the comparison of the shape of LDOS with t... |
In the context of random multiplicative energy cascade processes, we derive analytical expressions for translationally invariant one- and two-point cumulants in logarithmic field amplitudes. Such cumulants make it possible to distinguish between hitherto equally successful cascade generator models and hence supplement... |
A faithful description of the state of a complex dynamical network would require, in principle, the measurement of all its $d$ variables, an infeasible task for systems with practical limited access and composed of many nodes with high dimensional dynamics. However, even if the network dynamics is observable from a re... |
Gyrotactic algae are bottom heavy, motile cells whose swimming direction is determined by a balance between a buoyancy torque directing them upwards and fluid velocity gradients. Gyrotaxis has, in recent years, become a paradigmatic model for phytoplankton motility in flows. |
Understanding the interplay between different wave excitations, such as phonons and localized solitons, is crucial for developing coarse-grained descriptions of many-body, near-integrable systems. We treat the Fermi-Pasta-Ulam-Tsingou (FPUT) non-linear chain and show numerically that at short timescales, relevant to t... |
Dynamical control of excitable biological systems is often complicated by the difficult and unreliable task of pre-control identification of unstable periodic orbits (UPOs). Here we show that, for both chaotic and nonchaotic systems, UPOs can be located, and their dynamics characterized, during control. |
Chaotic systems are characterised by exponential separation between close-by trajectories, which in particular leads to deterministic unpredictability over an infinite time-window. It is now believed, that such butterfly effect is not fully relevant to account for the type of randomness observed in turbulence. |
This paper addresses the challenges of the Euler-Bernoulli beam theory regarding shortening and stretching assumptions. Certain boundary conditions, such as a cantilever with a horizontal spring attached to its end, result in beams that partly shorten or stretch, depending on the spring stiffness. |
This paper addresses the question of how Brownian-like motion can arise from the solution of a deterministic differential delay equation. To study this we analytically study the bifurcation properties of an apparently simple differential delay equation and then numerically investigate the probabilistic properties of c... |
We derive uniform approximations for contributions to Gutzwiller's periodic-orbit sum for the spectral density which are valid close to bifurcations of periodic orbits in systems with mixed phase space. There, orbits lie close together and give collective contributions, while the individual contributions of Gutzwi... |
In this communication we test the hypothesis that for some initial conditions the time evolution of surface waves according to the extended KdV equation (KdV2) exhibits signatures of the deterministic chaos. |
Dynamical Ensemble Equivalence between hydrodynamic dissipative equations and suitable time-reversible dynamical systems has been investigated in a class of dynamical systems for turbulence. The reversible dynamics is obtained from the original dissipative equations by imposing a global constraint. |
Upper bounds of the Hausdorff volume of scalar gradient field graphs are derived by means of geometric measure theory. The approach reproduces that scalar gradient fields along a mean imposed scalar gradient become space filling for sufficiently high values of Schmidt numbers Sc. |
We show that oscillation death as a specific type of oscillation suppression, which implies symmetry breaking, can be controlled by introducing time-delayed coupling. In particular, we demonstrate that time delay influences the stability of an inhomogeneous steady state, providing the opportunity to modulate the thres... |
Random band matrices relevant for open chaotic systems are introduced and studied. The scattering model based on such matrices may serve for the description of preequilibrium chaotic scattering. |
The turbulent energy flow of the onedimensional Majda-McLaughlin-Tabak equation is studied numerically. The system exhibits weak turbulence for weak driving forces, while weak turbulence coexists with strongly nonlinear intermittent collapses when the system is strongly driven. |
Chaos is shown to occur in the flexible shaft rotating-lifting (FSRL) system of the mono-silicon crystal puller. Chaos is, however, harmful for the quality of mono-silicon crystal production. |
Experimental observations of an almost symmetric electronic circuit show complicated sequences of bifurcations. These results are discussed in the light of a theory of imperfect global bifurcations. |
In this paper, we apply Lagrangian descriptors to study the invariant manifolds that emerge from the top of two barriers existing in the LiCN<->LiNC isomerization reaction. We demonstrate that the integration times must be large enough compared with the characteristic stability exponents of the periodic orbit un... |
A relevant problem in dynamics is to characterize how deterministic systems may exhibit features typically associated to stochastic processes. A widely studied example is the study of (normal or anomalous) transport properties for deterministic systems on a non-compact phase space. |
We consider a damped magnetic oscillator, consisting of a permanent magnet in a periodically oscillating magnetic field. A detailed investigation of the dynamics of this dissipative magnetic system is made by varying the field amplitude $A$. |
We recently presented a methodology for quantitatively reducing the risk and cost of executing electronic transactions in a bursty network environment such as the Internet. In the language of portfolio theory, time to complete a transaction and its variance replace the expected return and risk associated with a securi... |
One-dimensional Bernoulli mapping with hole is suggested to describe the regularities of the appearance of a chaotic set under the saddle-node scenario of the birth of the Smale--Williams hyperbolic attractor. In such a mapping, a non-trivial chaotic set (with non-zero Hausdorff dimension) arises in the general case a... |
Different scaling behavior has been reported in various shell models proposed for turbulent thermal convection. In this paper, we show that buoyancy is not always relevant to the statistical properties of these shell models even though there is an explicit coupling between velocity and temperature in the equations of ... |
A simple construction is presented, which generalises piecewise linear one-dimensional Markov maps to an arbitrary number of dimensions. The corresponding coupled map lattice, known as a simplicial mapping in the mathematical literature, allows for an analytical investigation. |
The problem of noise-induced escape from a metastable state arises in physics, chemistry, biology, systems engineering, and other areas. The problem is well understood when the underlying dynamics of the system obey detailed balance. |
Even as we understand for long that the world is quantal and buried in it is classical dynamics which is chaotic, finding eigenfunctions analytically from the the Schroedinger equation has turned out to be a near-impossibility. Here, we discover a class of chaotic quantum systems for which we obtain some analytically ... |
Inviscid invariants of flow equations are crucial in determining the direction of the turbulent energy cascade. In this work we investigate a variant of the three dimensional Navier-Stokes equations that shares exactly the same ideal invariants (energy and helicity) and the same symmetries (under rotations, reflexions... |
We study spatially periodic orbits for a coupled map lattice of sine circle maps with nearest neighbour coupling and periodic boundary conditions. The stability analysis for an arbitrary spatial period k is carried out in terms of the independent variables of the problem and the stability matrix is reduced to a neat b... |
Semiclassical approximations often involve the use of stationary phase approximations. This method can be applied when $\hbar$ is small in comparison to relevant actions or action differences in the corresponding classical system. |
A clear signature of classical chaoticity in the quantum regime is the fractal Weyl law, which connects the density of eigenstates to the dimension $D_0$ of the classical invariant set of open systems. Quantum systems of interest are often {\it partially} open (e.g., cavities in which trajectories are partially reflec... |
Wave chaos is demonstrated by studying a wave propagation in a periodically corrugated wave-guide. In the limit of a short wave approximation (SWA) the underlying description is related to the chaotic ray dynamics. |
Nonlinear time series analysis aims at understanding the dynamics of stochastic or chaotic processes. In recent years, quite a few methods have been proposed to transform a single time series to a complex network so that the dynamics of the process can be understood by investigating the topological properties of the n... |
We present an efficient method to solve Schrödinger's equation for perturbations of low rank. In particular, the method allows to calculate the level counting function with very little numerical effort. |
The conditions for emergence of Kolmogorov turbulence, and related weak wave turbulence, in finite size systems are analyzed by analytical methods and numerical simulations of simple models. The analogy between Kolmogorov energy flow from large to small spacial scales and conductivity in disordered solid state systems... |
We study the effect of the radiation parameter in the location, stability and orbital dynamics in the Lagrange configuration of the restricted four-body problem when one of the primaries is a radiating body. The equations of motion for the test particle are derived by assuming that the primaries revolve in the same pl... |
We consider a system of two Gross-Pitaevskii (GP) equations, in the presence of an optical-lattice (OL) potential, coupled by both nonlinear and linear terms. This system describes a Bose-Einstein condensate (BEC) composed of two different spin states of the same atomic species, which interact linearly through a reson... |
We study quantum-mechanical tunneling in mixed dynamical systems between symmetry-related phase space tori separated by a chaotic layer. Considering e.g. the annular billiard we decompose tunneling-related energy splittings and shifts into sums over paths in phase space. |
The pattern dynamics of the one-way coupled logistic lattice which can serve as a phenomenological model for open flow is investigated and shown to be extremely rich. For medium and large coupling strengths, we find spatially periodic, quasiperiodic and chaotic patterns with temporal periodicity and analyze their stab... |
We investigate the dependence of the escape rate on the position of a hole placed in uniformly hyperbolic systems admitting a finite Markov partition. We derive an exact periodic orbit formula for finite size Markov holes which differs from other periodic expansions in the literature and can account for additional dis... |
In this letter we are concerned with the possibility to approach the existence of solutions to a class of discontinuous dynamical systems of fractional order. In this purpose, the underlying initial value problem is transformed into a fractional set-valued problem. |
Motivated by bouncing motion of an inelastic particle on a vibrating board, a simple two-dimensional map is constructed and its behavior is studied numerically. In addition to the typical route to chaos through a periodic doubling bifurcation, we found peculiar behavior in the parameter region where two stable periodi... |
We report on partial and global generalized synchronization in exemplar bidirectionally coupled non-identical chaotic systems with multiple time delays. We derive conditions for such synchronization regimes. |
A coupled map lattice whose topology changes at each time step is studied. We show that the transversal dynamics of the synchronization manifold can be analyzed by the introduction of effective dynamical quantities. |
The Total Ozone Mapping Spectrometer (TOMS) database is subjected to an analysis in terms of the Karhunen-Loeve (KL) empirical eigenfunctions. The concentration variance spectrum is transformed into a wavenumber spectrum, $% E_c(k)$. |
Perturbations due to round-off errors in computer modeling are discontinuous and therefore one cannot use results like KAM theory about smooth perturbations of twist maps. We elaborate a special approximation scheme to construct two smooth periodic on the angle perturbations of the twist map, bounding the discretized ... |
The paper introduces a new 4d dynamical system leading to a typical 4d strange attractor. Its focal statement appears in its total disconnection from previous 3D nonlinear systems. |
Two symmetrically coupled logistic equations are proposed to mimic the competitive interaction between two species. The phenomena of coexistence, oscillations and chaos are present in this cubic discrete system. |
Semiclassical sum rules, such as the Gutzwiller trace formula, depend on the properties of periodic, closed, or homoclinic (heteroclinic) orbits. The interferences embedded in such orbit sums are governed by classical action functions and Maslov indices. |
We construct a model of an excitable medium with elastic rather than the usual diffusive coupling. We explore the dynamics of elastic excitable media, which we find to be dominated by low dimensional structures, including global oscillations, period-doubled pacemakers, and propagating fronts. |
Coupled map lattices of non-hyperbolic local maps arise naturally in many physical situations described by discretised reaction diffusion equations or discretised scalar field theories. As a prototype for these types of lattice dynamical systems we study diffusively coupled Tchebyscheff maps of N-th order which exhibi... |
A solvable model of noise effects on globally coupled limit cycle oscillators is proposed. The oscillators are under the influence of independent and additive white Gaussian noise. |
In this article we present an application of a method of control of Hamiltonian systems to the chaotic velocity diffusion of a cold electron beam interacting with electrostatic waves. We numerically show the efficiency and robustness of the additional small control term in restoring kinetic coherence of the injected e... |
We study fluctuation properties in the energy spectra of finite-size honeycomb lattices, graphene billiards, subject to the Haldane-model onsite potential and next-nearest neighbor interaction at critical points, referred to as Haldane graphene billiards in the following. The billiards had the shapes of a rectangular ... |
We consider a nonlinear area preserving Anosov map M on the torus phase space, which is the simplest example of a fully chaotic dynamics. We are interested in the quantum dynamics for long time, generated by the unitary quantum propagator Mq. |
We describe a simple mechanical system, a ball rolling along a specially-designed landscape, that mimics the dynamics of a well known phenomenon, the two-bounce resonance of solitary wave collisions, that has been seen in countless numerical simulations but never in the laboratory. We provide a brief history of the so... |
Area preserving maps provide the simplest and most accurate means to visualize and quantify the behavior of nonlinear systems. Convenience of the mapping equations of motion for investigation of transition to chaotic behavior in dynamics of classical atom in microwave field, transition to nonchaotic behavior in random... |
A simple example that I have been requested illustrates the statement in E-print <a href="https://arxiv.org/abs/nlin.CD/0201060" data-arxiv-id="nlin.CD/0201060" class="link-https">nlin.CD/0201060</a> that solutions of a smooth first order dynamic equation can be made Lyapunov stable at will by the choice of an appropri... |
Synchronization is a widespread phenomenon observed across natural and artificial networked systems. It often manifests itself by clusters of units exhibiting coincident dynamics. |
Quantum tunneling in a two-dimensional integrable map is studied. The orbits of the map are all confined to the curves specified by the one-dimensional Hamiltonian. |
One-dimensional chains are used as a fundamental model of condensed matter, and have constituted the starting point for key developments in nonlinear physics and complex systems. The pioneering work in this field was proposed by Fermi, Pasta, Ulam and Tsingou in the 50s in Los Alamos. |
New insight into the correspondence between Quantum Chaos and Random Matrix Theory is gained by developing a semiclassical theory for the autocorrelation function of spectral determinants. We study in particular the unitary operators which are the quantum versions of area preserving maps. |
We study the energy flow between a one dimensional oscillator and a chaotic system with two degrees of freedom in the weak coupling limit. The oscillator's observables are averaged over an initially microcanonical ensemble of trajectories of the chaotic system, which plays the role of an environment for the oscill... |
The dynamics of the four-body problem have attracted increasing attention in recent years. In this paper, we extend the basic equilateral four-body problem by introducing the effect of radiation pressure, Poynting-Robertson drag, and solar wind drag. |
We discuss the properties of eigenphases of S--matrices in random models simulating classically chaotic scattering. The energy dependence of the eigenphases is investigated and the corresponding velocity and curvature distributions are obtained both theoretically and numerically. A simple formula describing the velocit... |
A procedure to predict the occurrence of periodic clusters in a system of globally coupled maps displaying a constant mean field is presented. The method employs the analogy between a system of globally coupled maps and a single map driven by a constant force. |
Finite-dimensional wave turbulence refers to the chaotic dynamics of interacting wave `clusters' consisting of finite number of connected wave triads with exact three-wave resonances. We examine this phenomenon using the example of atmospheric planetary (Rossby) waves. |
We study the quantum manifestations of homogeneous and inhomogeneous oscillation suppression states in coupled identical quantum oscillators. We consider quantum van der Pol oscillators coupled via weighted mean-field diffusive coupling and using the formalism of open quantum system we show that depending upon the cou... |
We recently analyzed the voltage of the memristic circuit proposed by Muthuswamy and Chua by adding an external sinusoidal oscillation $\gamma\omega \cos\omega t$ to the ${\dot y}(t)\simeq {\dot i_L}(t)$, when the ${\dot x}(t)\simeq {\dot v_C}(t)$ is given by $y(t)/C$. <br>When $f_s<f_d$ we have observed that the H... |
This paper investigates the symmetry properties of basins of attraction and their boundaries in equivariant dynamical systems. While the symmetry groups of compact attractors are well understood, the corresponding analysis for non-compact basins and their boundaries has remained underdeveloped. |
The mode-fluctuation distribution $P(W)$ is studied for chaotic as well as for non-chaotic quantum billiards. This statistic is discussed in the broader framework of the $E(k,L)$ functions being the probability of finding $k$ energy levels in a randomly chosen interval of length $L$, and the distribution of $n(L)$, wh... |
A semiclassical approach to the universal ergodic spectral statistics in quantum star graphs is presented for all known ten symmetry classes of quantum systems. The approach is based on periodic orbit theory, the exact semiclassical trace formula for star graphs and on diagrammatic techniques. |
We derive variational equations to analyze the stability of synchronization for coupled near-identical oscillators. To study the effect of parameter mismatch on the stability in a general fashion, we define master stability equations and associated master stability functions, which are independent of the network struc... |
Unstable periodic orbits are known to originate scars on some eigenfunctions of classically chaotic systems through recurrences causing that some part of an initial distribution of quantum probability in its vicinity returns periodically close to the initial point. In the energy domain, these recurrences are seen to a... |
Transferring information from observations of a dynamical system to estimate the fixed parameters and unobserved states of a system model can be formulated as the evaluation of a discrete time path integral in model state space. The observations serve as a guiding potential working with the dynamical rules of the mode... |
We present an optimization process to estimate parameters in systems of ordinary differential equations from chaotic time series. The optimization technique is based on a variational approach, and numerical studies on noisy time series demonstrate that it is very robust and appropriate to reduce the complexity of the ... |
For low-dimensional chaotic attractors there is usually a single number of unstable dimensions for all of its periodic orbits and we can say such attractors exhibit "mono-chaos". In high-dimensional chaotic attractors, trajectories are prone to travel through quite different regions of phase space, some far mo... |
We consider a van der Pol-Mathieu (vdPM) equation with parametric forcing, which arises in a simplified model of dusty plasma with dust-charge fluctuation. We make a detailed numerical investigation and show that the system can be driven to chaos either through a period doubling cascade or though a subcritical pitchfo... |
We consider an autonomous system of partial differential equations for one-dimensional distributed medium with periodic boundary conditions. Dynamics in time consists of alternating birth and death of patterns with spatial phases transformed from one stage of activity to another by the doubly expanding circle map. |
We investigate classical and semiclassical aspects of codimension--two bifurcations of periodic orbits in Hamiltonian systems. A classification of these bifurcations in autonomous systems with two degrees of freedom or time-periodic systems with one degree of freedom is presented. |
We study the network replicator equation and characterize its fixed points on arbitrary graph structures for $2 \times 2$ symmetric games. We show a relationship between the asymptotic behavior of the network replicator and the existence of an independent vertex set in the graph and also show that complex behavior can... |
This paper concerns the classical dynamics of three coupled rotors: equal masses moving on a circle subject to attractive cosine inter-particle potentials. It is a simpler variant of the gravitational three-body problem and also arises as the classical limit of a model of coupled Josephson junctions. |
In this paper we present an influence of discontinuous coupling on the dynamics of multistable systems. Our model consists of two periodically forced oscillators that can interact via soft impacts. |
The influence of helicity on the stability of scaling regimes, on the effective diffusivity, and on the anomalous scaling of structure functions of a passive scalar advected by a Gaussian solenoidal velocity field with finite correlation time is investigated by the field theoretic renormalization group and operator pro... |
In this paper we show that the analysis of the dynamics in localized regions, i.e., sub-systems can be used to characterize the chaotic dynamics and the synchronization ability of the spatiotemporal systems. Using noisy scalar time-series data for driving along with simultaneous self-adaptation of the control paramete... |
In this paper a proposal is made of an adaptive coupling function for achieving synchronization between two lasers subject to optical <a href="http://feedback.Such" rel="external noopener nofollow" class="link-external link-http">this http URL</a> a control scheme requires knowledge of the systems' parameters. We ... |
We present a detailed review of the topics listed in the title, in particular using recent results of the authors. |
The interplay between chaos and thermalization in weakly non-integrable systems is a rich and complex subject. Interest in this area is further motivated by a desire to develop a unified picture of chaos for both quantum and classical systems. |
A non-autonomous system is proposed to model the seasonal pattern of dengue fever. <br>We found that an approximate threshold condition for infection persistence describes all possible behavior of the system. |
The coexistence of infinitely many attractors is called extreme multistability in dynamical systems. In coupled systems, this phenomenon is closely related to partial synchrony and characterized by the emergence of a conserved quantity. |
We study the relationship between the partial synchronous (PaS) state and the coupling structure in general dynamical systems. By the exact proof, we find the sufficient and necessary condition of the existence of PaS state for the coupling structure. |
The main signature of chaos in a quantum system is provided by spectral statistical analysis of the nearest neighbor spacing distribution and the spectral rigidity given by $\Delta_3(L)$. It is shown that some standard unfolding procedures, like local unfolding and Gaussian broadening, lead to a spurious increase of t... |
We show how to extract messages masked by a chaotic signal of a time-delay system with very high dimension and many positive Lyapunov exponents. Using a special embedding coordinate, the infinite dimensional phase space of the time-delay system is projected to a special three-dimensional space, which enables us to ide... |
Over the preceeding twenty years, the role of underlying classical dynamics in quantum mechanical tunneling has received considerable attention. A number of new tunneling phenomena have been uncovered that have been directly linked to the set of dynamical possibilities arising in simple systems that contain at least s... |
We develop a new approach to the theoretical treatment of the separatrix chaos, using a special analysis of the separatrix map. The approach allows us to describe boundaries of the separatrix chaotic layer in the Poincaré section and transport within the layer. |
A manifestly relativistically covariant form of the van der Pol oscillator in 1+1 dimensions is studied. We show that the driven relativistic equations, for which $x$ and $t$ are coupled, relax very quickly to a pair of identical decoupled equations, due to a rapid vanishing of the ``angular momentum'' (the bo... |
Transport from nutrient-rich coastal upwellings is a key factor influencing biological activity in surrounding waters and even in the open ocean. The rich upwelling in the North-Western African coast is known to interact strongly with the wake of the Canary islands, giving rise to filaments and other mesoscale structu... |
We consider a finite, closed and selfbound many--body system in which a collective degree of freedom is excited. The redistribution of energy and momentum into a finite number of the non-collective degrees of freedom is referred to as spreading as opposed to damping in open systems. |
We present a personal view of the state of the art in turbulence research. We summarize first the main achievements in the recent past, and then point ahead to the main challenges that remain for experimental and theoretical efforts. |
We study the completely synchronized states (CSSs) of a system of coupled logistic maps as a function of three parameters: interaction strength ($\varepsilon$), range of the interaction ($\alpha$), that can vary from first-neighbors to global coupling, and a parameter ($\beta$) that allows to scan continuously from non... |
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