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We report on a switching synchronization phenomenon in one-dimensional memristive networks, which occurs when several memristive systems with different switching constants are switched from the high- to low-resistance state. Our numerical simulations show that such a collective behavior is especially pronounced when the applied voltage slightly exceeds the combined threshold voltage of memristive systems. Moreover, a finite increase in the network switching time is found compared to the average switching time of individual systems. An analytical model is presented to explain our observations. Using this model, we have derived asymptotic expressions for memory resistances at short and long times, which are in excellent agreement with results of our numerical simulations. [ABSTRACT FROM AUTHOR]

We demonstrate an unexpected connection between isotropic turbulence and wall-bounded shear flows. We perform direct numerical simulations of isotropic turbulence forced at large scales at moderate Reynolds numbers and observe sudden transitions from a chaotic dynamics to a spatially simple flow, analogous to the laminar state in wall bounded shear flows. We find that the survival probabilities of turbulence are exponential and the typical lifetimes increase superexponentially with the Reynolds number. Our results suggest that both isotropic turbulence and wall-bounded shear flows qualitatively share the same phase-space dynamics. [ABSTRACT FROM AUTHOR]

An effective method of controlling chaos is proposed. The control mechanism of the proposed method can be interpreted as the synchronization of a chaotic system with a system of harmonic oscillators. It is a practically noninvasive method that does not change the solution of dynamical systems, but stabilizes their periodic behavior by applying only small perturbations. The proposed method has fairly simple structure that suggests a clear stabilizing mechanism, and allows a straightforward evaluation of stability properties. This control scheme can be implemented experimentally even if the dynamical system is not analytically known. The efficiency of the proposed method is demonstrated through numerical simulation as well as experimental implementation. [ABSTRACT FROM AUTHOR]

We discuss the occurrence of chimera states in networks of nonlocally coupled bistable oscillators, in which individual subsystems are characterized by the coexistence of regular (a fixed point or a limit cycle) and chaotic attractors. By analyzing the dependence of the network dynamics on the range and strength of coupling, we identify parameter regions for various chimera states, which are characterized by different types of chaotic behavior at the incoherent interval. Besides previously observed chimeras with space-temporal and spatial chaos in the incoherent intervals we observe another type of chimera state in which the incoherent interval is characterized by a central interval with standard space-temporal chaos and two narrow side intervals with spatial chaos. Our findings for the maps as well as for time-continuous van der Pol-Duffing's oscillators reveal that this type of chimera states represents characteristic spatiotemporal patterns at the transition from coherence to incoherence. [ABSTRACT FROM AUTHOR]

We develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting point, is described by a Markov chain, which in the limit of large system sizes is shown to be very well-approximated by a Fokker-Planck-like equation, or equivalently by a set of stochastic difference equations. This formalism is applied to the specific case of two species: one predator species and its prey species. Quasicycles, stochastic cycles sustained and amplified by the demographic noise, previously found in continuous-time predator-prey models are shown to exist, and their behavior predicted from a linear noise analysis is shown to be in very good agreement with simulations. The effects of the noise on other attractors in the corresponding deterministic map, such as periodic cycles, quasiperiodicity, and chaos, are also investigated. [ABSTRACT FROM AUTHOR]

A direct numerical simulation of the three-dimensional elektrokinetic instability near a charge-selective surface (electric membrane, electrode, or system of micro- or nanochannels) has been carried out and analyzed. A special finite-difference method has been used for the space discretization along with a semi-implicit 31/3 -step Runge-Kutta scheme for the integration in time. The calculations employ parallel computing. Three characteristic patterns, which correspond to the overlimiting currents, are observed: (a) two-dimensional electroconvective rolls, (b) three-dimensional regular hexagonal structures, and (c) three-dimensional structures of spatiotemporal chaos, which are a combination of unsteady hexagons, quadrangles, and triangles. The transition from (b) to (c) is accompanied by the generation of interacting two-dimensional solitary pulses. [ABSTRACT FROM AUTHOR]

We study the chaotic motion of a small rigid sphere, lighter than the fluid in a three-dimensional vortex of finite height. Based on the results of Eulerian and Lagrangian measurements, a sequence of models is set up. The time-independent model is a generalization of the Burgers vortex. In this case, there are two types of attractors for the particle: a fixed point on the vortex axis and a limit cycle around the vortex axis. Time dependence might combine these regular attractors into a single chaotic attractor, however its robustness is much weaker than what the experiments suggest. To construct an aperiodically time-dependent advection dynamics in a simple way, Gaussian noise is added to the particle velocity in the numerical simulation. With an appropriate choice of the noise properties, mimicking the effect of local turbulence, a reasonable agreement with the experimentally observed particle statistics is found. [ABSTRACT FROM AUTHOR]

A neural-network model is proposed as a test bed for the characterization of the chaotic dynamics emerging in a context where the coupling is, on the average, neither excitatory nor inhibitory. The proposed discrete-time model generalizes within a single framework two different setups previously studied in the literature. With the help of theoretical mean field arguments and numerical simulations on GPUs, we characterize the transition and show that the chaotic dynamics is extensive (i.e., that the number of active degrees of freedom is proportional to the network size) from the very beginning. Besides the coupling strength, two parameters play a crucial role: (1) one controls the local dissipation and determines the shape of the initial part of the Lyapunov spectrum as well as the shape of the correlation function; (2) the other, which corresponds to the amplitude of an effective random field, determines the nature of the transition. [ABSTRACT FROM AUTHOR]

Despite several experiments on chaotic quantum transport in two-dimensional systems such as semiconductor quantum dots, corresponding quantum simulations within a real-space model have been out of reach so far. Here we carry out quantum transport calculations in real space and real time for a two-dimensional stadium cavity that shows chaotic dynamics. By applying a large set of magnetic fields we obtain a complete picture of magnetoconductance that indicates fractal scaling. In the calculations of the fractality we use detrended fluctuation analysis--a widely used method in time-series analysis--and show its usefulness in the interpretation of the conductance curves. Comparison with a standard method to extract the fractal dimension leads to consistent results that in turn qualitatively agree with the previous experimental data. [ABSTRACT FROM AUTHOR]

Plasma defocusing and higher-order Kerr effects on multiple filamentation and pattern formation of ultrashort laser pulse propagation in air are investigated. Linear analyses and numerical results show that these two saturable nonlinear effects can destroy the coherent evolution of the laser field, and small-scale spatial turbulent structures rapidly appear. For the two-dimensional case, numerical simulations show that blow-up-like solutions, spatial chaos, and pseudorecurrence can appear at higher laser intensities if only plasma defocusing is included. These complex patterns result from the stochastic evolution of the higher- or shorter-wavelength modes of the laser light spectrum. From the viewpoint of nonlinear dynamics, filamentation can be attributed to the modulational instability of these spatial incoherent localized structures. Furthermore, filament patterns associated with multiphoton ionization of the air molecules with and without higher-order Kerr effects are compared. [ABSTRACT FROM AUTHOR]

The dynamics of a spring-block train placed on a moving conveyor belt is investigated both by simple experiments and computer simulations. The first block is connected by a spring to an external static point and, due to the dragging effect of the belt, the blocks undergo complex stick-slip dynamics. A qualitative agreement with the experimental results can be achieved only by taking into account the spatial inhomogeneity of the friction force on the belt's surface, modeled as noise. As a function of the velocity of the conveyor belt and the noise strength, the system exhibits complex, self-organized critical, sometimes chaotic, dynamics and phase transition-like behavior. Noise-induced chaos and intermittency is also observed. Simulations suggest that the maximum complexity of the dynamical states is achieved for a relatively small number of blocks (around five). [ABSTRACT FROM AUTHOR]

We examine the effects of symmetry-preserving and -breaking interactions in a drive-response system where the response has an invariant symmetry in the absence of the drive. Subsequent to the onset of generalized synchronization, we find that there can be more than one stable attractor. Numerical as well as analytical results establish the presence of phase synchrony in such coexisting attractors. These results are robust to external noise. [ABSTRACT FROM AUTHOR]

Recent studies of network science have revealed the sensitive dependence of network collective behaviors on structures; here we employ this feature of topological sensitivity for the purpose of pattern control. By simple models of networked chaotic oscillators, we are able to argue and demonstrate that, by manipulating just a single link in the network, the synchronous patterns of the system can be effectively adjusted or controlled. In particular, by changing the weight or the connection of a shortcut link in the network, we find not only that various stable synchronous patterns can be generated from the system but also that the synchronous patterns can be successfully switched among different forms. The stability of the synchronous patterns is analyzed by the method of eigenvalue analysis, and the feasibility of the control is verified by numerical simulations. Our study provides a step forward to the control of sophisticated collective behaviors in more complex networks, as well as insights to the evolution and function of some realistic complex systems. [ABSTRACT FROM AUTHOR]

Symbolic dynamics method and time reversal asymmetry analysis are both important approaches in the study of heartbeat interval series. However, there is limited research work reported on combining these two methods. We provide a method of time reversal asymmetry analysis which focuses on the differences between the forward and backward embedding "m words" after the operation of equiprobable symbolization. To investigate the total amplitude as well as the distribution features of the difference, four indices are proposed. Based on the application to simulation series, we found that these measures can successfully detect time reversal asymmetry in chaos series. With application to human heartbeat interval series (RR series), it is suggested that the distribution features of the forward-backward difference can sensitively capture the dynamical changes caused by diseases or aging. In particular, the index ED, which reflects the random degree of the forward-backward difference distribution, can significantly discriminate healthy subjects from diseased ones. We conclude that RR series from healthy subjects show more asymmetry in temporal structure on the original time scale from the perspective of equiprobable symbolization, whereas diseases account for loss of this asymmetry. [ABSTRACT FROM AUTHOR]

Semiclassical results are usually expected to be valid in the semiclassical regime. An interesting question is, in models in which appropriate effective Planck constants can be introduced, to what extent will a semiclassical prediction stay valid when the effective Planck constant is increased? In this paper, we numerically study this problem, focusing on semiclassical predictions for the decay of the quantum Loschmidt echo in deep quantum regions. Our numerical simulations, carried out in the chaotic regime in the sawtooth model and in the kicked rotator model and also in the critical region of a one-dimensional Ising chain in transverse field, show that the semiclassical predictions may work even in deep quantum regions, particularly for perturbation strength in the so-called Fermi-Golden-Rule regime. [ABSTRACT FROM AUTHOR]

In this paper we introduce a multiscale symbolic information-theory approach for discriminating nonlinear deterministic and stochastic dynamics from time series associated with complex systems. More precisely, we show that the multiscale complexity-entropy causality plane is a useful representation space to identify the range of scales at which deterministic or noisy behaviors dominate the system's dynamics. Numerical simulations obtained from the well-known and widely used Mackey-Glass oscillator operating in a high-dimensional chaotic regime were used as test beds. The effect of an increased amount of observational white noise was carefully examined. The results obtained were contrasted with those derived from correlated stochastic processes and continuous stochastic limit cycles. Finally, several experimental and natural time series were analyzed in order to show the applicability of this scale-dependent symbolic approach in practical situations. [ABSTRACT FROM AUTHOR]

A model of self-driven particles similar to the Vicsek model [Phys. Rev. Lett. 75, 1226 (1995)] but with metric-free interactions is studied by means of a novel Enskog-type kinetic theory. In this model, N particles of constant speed v0 try to align their travel directions with the average direction of a fixed number of closest neighbors. At strong alignment a global flocking state forms. The alignment is defined by a stochastic rule, not by a Hamiltonian. The corresponding interactions are of genuine multibody nature. The theory is based on a Master equation in 3/V-dimensional phase space, which is made tractable by means of the molecular chaos approximation. The phase diagram for the transition to collective motion is calculated and compared to direct numerical simulations. A linear stability analysis of a homogeneous ordered state is performed using the kinetic but not the hydrodynamic equations in order to achieve high accuracy. In contrast to the regular metric Vicsek-model no instabilities occur. This confirms previous direct simulations that, for Vicsek-like models with metric-free interactions, there is no formation of density bands and that the flocking transition is continuous. [ABSTRACT FROM AUTHOR]

Numerical simulations of the geodynamo in the presence of heterogeneous heating are presented. We study the dynamics and the structure of the magnetic field when the equatorial symmetry of the flow is broken. If the symmetry breaking is sufficiently strong, the m = 0 axial dipolar field is replaced by a hemispherical magnetic field, dominated by an oscillating m = 1 magnetic field. Moreover, for moderate symmetry breaking, a bistability between the axial and the equatorial dipole is observed. In this bistable regime, the axial magnetic field exhibits chaotic switches of its polarity, involving the equatorial dipole during the transition period. This new scenario for magnetic field reversals is discussed within the framework of Earth's dynamo [ABSTRACT FROM AUTHOR]

Using large-scale parallel numerical simulations we explore spatiotemporal chaos in Rayleigh-Bénard convection in a cylindrical domain with experimentally relevant boundary conditions. We use the variation of the spectrum of Lyapunov exponents and the leading-order Lyapunov vector with system parameters to quantify states of high-dimensional chaos in fluid convection. We explore the relationship between the time dynamics of the spectrum of Lyapunov exponents and the pattern dynamics. For chaotic dynamics we find that all of the Lyapunov exponents are positively correlated with the leading-order Lyapunov exponent, and we quantify the details of their response to the dynamics of defects. The leading-order Lyapunov vector is used to identify topological features of the fluid patterns that contribute significantly to the chaotic dynamics. Our results show a transition from boundary-dominated dynamics to bulk-dominated dynamics as the system size is increased. The spectrum of Lyapunov exponents is used to compute the variation of the fractal dimension with system parameters to quantify how the underlying high-dimensional strange attractor accommodates a range of different chaotic dynamics. [ABSTRACT FROM AUTHOR]

We investigate the spatio-temporal dynamics of coupled chaotic systems with nonlocal interactions, where each element is coupled to its nearest neighbors within a finite range. Depending upon the coupling strength and coupling radius, we find characteristic spatial patterns such as wavelike profiles and study the transition from coherent to incoherence leading to spatial chaos. We analyze the origin of this transition based on numerical simulations and support the results by theoretical derivations, identifying a critical coupling strength and a scaling relation of the coherent profiles. To demonstrate the universality of our findings, we consider time-discrete as well as time-continuous chaotic models realized as a logistic map and a Rössler or Lorenz system, respec tively. Thereby, we establish the coherence-incoherence transition in networks of coupled identical oscillators. [ABSTRACT FROM AUTHOR]

We consider here a recent conjecture stating that correlation functions and tail probabilities of finite time Lyapunov exponents would have the same power law decay in weakly chaotic systems. We demonstrate that this conjecture fails for a generic class of maps of the Pomeau-Manneville type. We show further that, typically, the decay properties of such tail probabilities do not provide significant information on key aspects of weakly chaotic dynamics such as ergodicity and instability regimes. Our approaches are firmly based on rigorous results, particularly the Aaronson-Darling-Kac theorem, and are also confirmed by exhaustive numerical simulations. [ABSTRACT FROM AUTHOR]

A chaotic network of size N with delayed interactions which resembles a pseudoinverse associative memory neural network is investigated. For a load α = P/N < 1, where P stands for the number of stored patterns, the chaotic network functions as an associative memory of 2 P attractors with macroscopic basin of attractions which decrease with α. At finite α, a chaotic spin-glass phase exists, where the number of distinct chaotic attractors scales exponentially with N. Each attractor is characterized by a coexistence of chaotic behavior and freezing of each one of the N chaotic units or freezing with respect to the P patterns. Results are supported by large scale simulations of networks composed of Bernoulli map units and Mackey-Glass time delay differential equations. [ABSTRACT FROM AUTHOR]

We investigate decoherence in quantum systems coupled via dephasing-type interactions to an arbitrary environment with chaotic underlying classical dynamics. The coherences of the reduced state of the central system written in the preferential energy eigenbasis are quantum Loschmidt echoes, which in the strong coupling regime are characterized at long time scales by fluctuations around a constant mean value. We show that due to the chaotic dynamics of the environment, the mean value and the width of the Loschmidt-echo fluctuations are inversely proportional to the quantity we define as the effective Hilbert-space dimension of the environment, which in general is smaller than the dimension of the entire available Hilbert space. Nevertheless, in the semiclassical regime this effective Hilbert-space dimension is in general large, in which case even a chaotic environment with few degrees of freedom produces decoherence without revivals. Moreover we show that in this regime the environment leads the central system to equilibrate to the time average of its reduced density matrix, which corresponds to a diagonal state in the preferential energy eigenbasis. For the case of two uncoupled, initially entangled central systems that interact with identical local quantum environments with chaotic underlying classical dynamics, we show that in the semiclassical limit the equilibration state is arbitrarily close to a separable state. We confirm our results with numerical simulations in which the environment is modeled by the quantum kicked rotor in the chaotic regime. [ABSTRACT FROM AUTHOR]

The decay of a passive scalar in a three-dimensional chaotic flow is studied using high-resolution numerical simulations. The (volume-preserving) flow considered is a three-dimensional extension of the randomized alternating sine flow employed extensively in studies of mixing in two dimensions. It is used to show that theoretical predictions for two-dimensional flows with small diffusivity carry over to three dimensions even though the stretching properties differ significantly. The variance decay rate, scalar field structure, and time evolution of statistical moments confirm that there are two distinct regimes of scalar decay: a locally controlled regime, which applies when the domain size is comparable to the characteristic length scale of the velocity field, and a globally controlled regime, which applies when the domain is larger. Asymptotic predictions for the variance decay rate in both regimes show excellent agreement with the numerical results. Consideration of both the forward flow and its time reverse makes it possible to compare the scalar evolution in flows with one or two expanding directions; simulations confirm the theoretical prediction that the decay rate of the scalar is the same in both flows, despite the very different scalar field structures. [ABSTRACT FROM AUTHOR]

Excitable systems display memory, but how memory affects the excitation dynamics of such systems remains to be elucidated. Here we use computer simulation of cardiac action potential models to demonstrate that memory can cause dynamical instabilities that result in complex excitation dynamics and chaos. We develop an iterated map model that correctly describes these dynamics and show that memory converts a monotonic first return map of action potential duration into a nonmonotonic one, resulting in a period-doubling bifurcation route to chaos. [ABSTRACT FROM AUTHOR]

We present a characterization of short-term stability of Kauffman's NK (random) Boolean networks under arbitrary distributions of transfer functions. Given such a Boolean network where each transfer function is drawn from the same distribution, we present a formula that determines whether short-term chaos (damage spreading) will happen. Our main technical tool which enables the formal proof of this formula is the Fourier analysis of Boolean functions, which describes such functions as multilinear polynomials over the inputs. Numerical simulations on mixtures of threshold functions and nested canalyzing functions demonstrate the formula's correctness. [ABSTRACT FROM AUTHOR]

We present the experimental evidence of deterministic coherence resonance in unidirectionally coupled two and three Rössler electronic oscillators with mismatch between their natural frequencies. The regularity in both the amplitude and the phase of chaotic fluctuations is experimentally proven by the analyses of normalized standard deviations of the peak amplitude and interpeak interval and Lyapunov exponents. The resonant chaos suppression appears when the coupling strength is increased and the oscillators are in phase synchronization. In two coupled oscillators, the coherence enhancement is associated with negative third and fourth Lyapunov exponents, while the largest first and second exponents remain positive. Distinctly, in three oscillators coupled in a ring, all exponents become negative, giving rise to periodicity. Numerical simulations are in good agreement with the experiments. [ABSTRACT FROM AUTHOR]