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We consider equal-mass periodic Toda oscillators with balanced loss-gain for two and three particles. The two-particle system is integrable. The three-particle equal-mass periodic Toda lattice is considered in presence of balanced loss-gain and velocity mediated coupling. The system is Hamiltonian for specific values of the coupling constants. The generalized momentum is the second integral of motion and study of Poincaré section indicates its integrability in certain region of the parameter-space. The generic model admits both non-chaotic and chaotic solutions. The chaos in the system with vanishing velocity mediated coupling is solely induced due to the presence of balanced loss-gain, since undriven equal-mass Toda lattice is non-chaotic. The chaotic behavior is studied in detail for the generic system. • An integrable two particle Toda Lattice with balanced loss-gain is presented. • Balanced loss-gain induced chaos is shown to exist in a 3-particle Toda Lattice. • The 3-particle Toda lattice is Hamiltonian under certain conditions. • Detailed numerical investigations on the regular and chaotic dynamics are presented. [ABSTRACT FROM AUTHOR]

We explore the sensitivity of repulsive and attractive Casimir interactions on thermal fluctuations in topological insulator materials, and the associated effects on non-linear actuation towards chaotic motion. For system at low temperature and applied magnetization in the same direction, by increasing the temperature the sensitivity of the Casimir force to the magnetization, at large separations, weakens. Moreover, by increasing the temperature the repulsive force vanishes for weak magnetization. Furthermore, for conservative systems the stable actuation area for high temperature does not show strong sensitivity to changes of the magnetization and the magnetoelectric effect. For non-conservative system with weak magnetization in the same direction leading to attractive Casimir forces, increment of the temperature increases the possibility for occurrence of chaotic motion. • The influence of the thermal correction is different for systems with magnetizations leading to attractive and repulsive forces. • At low temperature, increment of the temperature weakens the sensitivity of the attractive Casimir force to the magnetization. • By increasing the temperature, the repulsive force vanishes for weak magnetization in the opposite direction. • Decreasing the temperature does not provide an efficient method to reduce chaotic motion for systems with strong magnetization. [ABSTRACT FROM AUTHOR]

Highlights • DNA encoding is introduced into the field of optical encryption. • An optical XOR gate is used to achieve XOR operation in ultra-fast DNA encryption. • The DNA rules used for data encoding are different in each row and column, which enhances the security of system. Abstract We propose an optical image encryption scheme based on the Deoxyribonucleic Acid (DNA) theory and the double random phase encoding (DRPE) technique. The piecewise linear chaotic map (PWLCM) is used to generate key images and random phase masks, and to determine DNA encoding rules. In order to achieve ultra-fast DNA encryption, we propose using an optical exclusive-OR (XOR) gate to achieve XOR operation in DNA encryption. Different plaintexts use different initial values of PWLCM, which are generated by Message Digest Algorithm 5 (MD5). The plaintext is encrypted by two rounds of DNA and then by DRPE to form a ciphertext. Numerical simulation and the analysis of attacks on encrypted image are implemented to demonstrate the security and validity of the proposed approach. [ABSTRACT FROM AUTHOR]

Highlights • Permutation instead of raw vector is adopted to simplify time irreversibility analysis. • Considering the forbidden permutation, a subtraction-based parameter, Y S , is proposed. • Chaotic and reversible processes and their surrogate data validate Y S. • Healthy and diseased brain activities manifest time irreversibility. • Epilepsy leads loss of time irreversibility of EEG during seizure-free intervals. Abstract To simplify the quantification of time irreversibility, we employ order patterns instead of the raw multi-dimension vectors in time series, and considering the existence of forbidden permutation, we propose a subtraction-based parameter, Y S , to measure the probabilistic differences between symmetric permutations for time irreversibility. Two chaotic models, the logistic and Henon systems, and reversible Gaussian process and their surrogate data are used to validate the time-irreversible measure, and time irreversibility of epileptic EEGs from Nanjing General Hospital is detected by the parameter. Test results prove that it is promising to quantify time irreversibility by measuring the subtraction-based probabilistic differences between symmetric order patterns, and our findings highlight the manifestation of nonlinearity of whether healthy or diseased EEGs and suggest that the epilepsy leads to a decline in the nonlinearity of brain electrical activities during seize-free intervals. [ABSTRACT FROM AUTHOR]

Abstract A model for inhomogeneously coupled logistic maps is considered to find some critical exponents in the transition from inhomogeneous steady state to spatiotemporal chaos through spatiotemporal intermittency. The laminar state in the model is described by inhomogeneous steady state with spatial period two. We obtain a complete set of static exponents which match with the corresponding directed percolation (DP) values in (1+1) dimension. We also find four nonuniversal spreading exponents in which three exponents are in agreement with DP values. The model in which absorbing state is inhomogeneous steady state, contributes a new example in evidence of Pomeau's [18] conjecture that the onset of STI in a deterministic system belongs to DP universality class. Highlights • DP universality is found in an inhomogeneous system. • The absorbing state is inhomogeneous which is steady but periodic in space with period two. • The values of four static exponents and three spreading exponents are consistent with the corresponding DP values. • Three scaling relations and three scaling functions are established. [ABSTRACT FROM AUTHOR]

Abstract Stochastic resonance is a phenomenon that a weak signal can be amplified and optimized by the assistance of noise in bistable system. There is still not enough research on the mutual interplay among system, noise and signal. In this paper, we study the role of every parameter in nonlinear transfer and discover chaos phenomenon in stochastic resonance. To measure the influence of chaos, a trajectory decision function was proposed. Based on this function, we found two forms of stochastic resonance, clockwise resonance and counterclockwise resonance. Highlights • In this paper, we study the role of every parameter in stochastic resonance and discover chaos phenomenon in it. • A trajectory decision function was proposed to measure the influence of chaos. • Based on this function, we found two forms of stochastic resonance, clockwise resonance and counterclockwise resonance. [ABSTRACT FROM AUTHOR]

Motivated by an important practical significance, we analyze the noise-induced El Niño evolutionary equations. Our analysis based on the evaluation of largest Lyapunov exponents demonstrates the new effects of deterministic and stochastic dynamics of the El Niño–Southern Oscillation Events. We show that the non-linear deterministic model possesses either a multiturn limit cycle with regular self-oscillations or chaotic oscillations depending on slight variations of one of the main system parameters – the mean tropical easterlies. It is revealed that in the presence of noise, transformations of regular oscillations into chaotic ones are observed. [ABSTRACT FROM AUTHOR]

This research investigates the identification problem of fractional-order chaotic systems under stable distribution noises. A powerful metaheuristic optimization method called composite differential evolution is used for the identification of the fractional-order Lorenz and Chen systems in the noisy environment, where the structure, parameters, orders and initial values of the systems are all unknown. The identification accuracy is examined when the noise follows the three special cases of stable distributions, i.e., Gaussian, Cauchy and Lévy distributions. In addition, the impact of the four parameters of stable distributions on the identification accuracy is discussed. The experimental results show that the identification error becomes larger when the noise switches from Gaussian to Cauchy and Lévy distributions. The results also turn out that the location of the stable distribution noise plays the most substantial role in the identification accuracy. [ABSTRACT FROM AUTHOR]

As a new technique for authentication and key generation, physically unclonable function (PUF) has attracted considerable attentions, with extensive research results achieved already. To resist the popular machine learning modeling attacks, a framework to enhance the security of PUFs is proposed. The basic idea is to combine PUFs with a chaotic system of which the response is highly sensitive to initial conditions. For this framework, a specific construction which combines the common arbiter PUF circuit, a converter, and the Chua's circuit is given to implement a more secure PUF. Simulation experiments are presented to further validate the framework. Finally, some practical suggestions for the framework and specific construction are also discussed. [ABSTRACT FROM AUTHOR]

We study the phenomena of chimera destruction and inducing of chimera-like states in an ensemble of nonlocally coupled chaotic Rössler oscillators under an external harmonic force. The localized harmonic influence can lead to both destruction and changing of the spatial topology of chimeras. At the same time this influence can cause the emergence of stable chimera-like states ( induced chimeras ) for the regime of partial coherent chaos. Induced chimeras are also observed for the global influence. We show the possibility of controlling the chimera-like state topology by varying the parameters of localized external harmonic influence. [ABSTRACT FROM AUTHOR]

A new dynamical system based on Thomas' system is described with infinitely many strange attractors on a 3-D spatial lattice. The mechanism for this multistability is associated with the disturbed offset boosting of sinusoidal functions with different spatial periods. Therefore, the initial condition for offset boosting can trigger a bifurcation, and consequently infinitely many attractors emerge simultaneously. One parameter of the sinusoidal nonlinearity can increase the frequency of the second order derivative of the variables rather than the first order and therefore increase the Lyapunov exponents accordingly. We show examples where the lattice is periodic and where it is quasiperiodic, that latter of which has an infinite variety of attractor types. [ABSTRACT FROM AUTHOR]

The study of the synchronous stability of two coupled Rössler attractors sometimes can be effectively described by approximating the trajectory on the attractor as a planar outward spiral. We show that this is true only when one is dealing with the spiral-type attractor. But when the equally important funnel-type attractor is encountered, a properly constructed time-weighted average must be used to yield a prediction that agrees well with numerical results. We also show analytically how the separation vector evolves in time, and demonstrate why this study matters when one tries to perform the time-weighted average. [ABSTRACT FROM AUTHOR]

A Monte Carlo investigation is made in a dissipative bouncer model to describe some statistical properties for chaotic dynamics as a function of the control parameters. The dynamics of the system is described via a two dimensional mapping for the variables velocity of the particle and phase of the moving wall at the instant of the impact. A small stochastic noise is introduced in the time of flight of the particle as an attempt to investigate the evolution of the system without the need to solve transcendental equations. We show that average values along the chaotic dynamics do not strongly depend on the noise size. It allows us to propose a Monte Carlo like simulation that lead to calculate average values for the observables with great accuracy and fast simulations. [ABSTRACT FROM AUTHOR]

In this Letter, we report the influences of thermal time-lag on the onset of convection, its bifurcations and chaos of a horizontal layer of Boussinesq fluid heated underneath taking non-Fourier Cattaneo–Christov hyperbolic model for heat propagation. A five-dimensional nonlinear system is obtained for a low-order Galerkin expansion, and it reduces to Lorenz system for Cattaneo number tending to zero. The linear stability agreed with existing results that depend on Cattaneo number C . It also gives a threshold Cattaneo number, C T , above which only oscillatory solutions can persist. The oscillatory solutions branch terminates at the subcritical steady branch with a heteroclinic loop connecting a pair of saddle points for subcritical steady-state solutions. For subcritical onset of convection two stable solutions coexist, that is, hysteresis phenomenon occurs at this stage. The steady solution undergoes a Hopf bifurcation and is of subcritical type for small value of C , while it becomes supercritical for moderate Cattaneo number. The system goes through period-doubling/noisy period-doubling transition to chaos depending on the control parameters. There after the system exhibits Shil'nikov chaos via homoclinic explosion. The complexity of spiral strange attractor is analyzed using fractal dimension and return map. [ABSTRACT FROM AUTHOR]

In this paper, the identification problem of fractional-order chaotic systems is proposed and investigated via an evolutionary optimization approach. Different with other studies to date, this research focuses on the identification of fractional-order chaotic systems with not only unknown orders and parameters, but also unknown initial values and structure. A group of fractional-order chaotic systems, i.e., Lorenz, Lü, Chen, Rössler, Arneodo and Volta chaotic systems, are set as the system candidate pool. The identification problem of fractional-order chaotic systems in this research belongs to mixed integer nonlinear optimization in essence. A powerful evolutionary algorithm called composite differential evolution (CoDE) is introduced for the identification problem presented in this paper. Extensive experiments are carried out to show that the fractional-order chaotic systems with unknown initial values and structure can be successfully identified by means of CoDE. [ABSTRACT FROM AUTHOR]

Dynamics arising in the Hindmarsh–Rose model are considered from a novel perspective. We study qualitative changes that occur as the time scale of the slow variable increases taking the system far from the slow-fast scenario. We see how the structure of spike-adding still persists far from the singular case but the geometry of the bifurcations changes notably. Particular attention is paid to changes in the shape of the homoclinic bifurcation curves and the disappearance of Inclination-Flip codimension-two points. These transformations seem to be linked to the way in which the spike-adding takes place, the changing from fold/hom to fold/Hopf bursting behavior and also with the way in which the chaotic regions evolve as the time scale of the slow variable increases. [ABSTRACT FROM AUTHOR]

Phase control of chaos is a powerful technique but little is known about its physical constraints, relevant for real systems. As a fact, it has not been explored whether this technique can also be applied when the controlling perturbation is not harmonic. Here we apply phase control on a driven double well Duffing oscillator using periodic rectangular pulsed perturbations instead of the classical sinusoidal perturbations. Experimental measurements and numerical simulations show that this kind of perturbation is also able to stabilize the chaotic orbits for an adequate selection of the phase. Furthermore, as the duty cycle of the perturbation (that is, the fraction of the time that the periodically pulsed control is active) is increased, two separate regimes occur. In the first one, the perturbations leading to stabilization of periodic solutions are of constant energy (taken as the product of the duty cycle and the amplitude) and in the second one, a saturation phenomenon occurs, implying that increasing energy values of the perturbations are wasted. Our results unveil the versatility of the pulsed phase control scheme and the importance of energy constraints. [ABSTRACT FROM AUTHOR]

We study the 3-d Bohmian trajectories of a quantum system of three harmonic oscillators. We focus on the mechanism responsible for the generation of chaotic trajectories. We demonstrate the existence of a 3-d analogue of the mechanism found in earlier studies of 2-d systems [1,2] , based on moving 2-d ‘nodal point–X-point complexes’. In the 3-d case, we observe a foliation of nodal point–X-point complexes, forming a ‘3-d structure of nodal and X-points’. Chaos is generated when the Bohmian trajectories are scattered at one or more close encounters with such a structure. [ABSTRACT FROM AUTHOR]

In order to study the behaviour of discrete dynamical systems under adiabatic cyclic variations of their parameters, we consider discrete versions of adiabatically-rotated rotators. Parallelling the studies in continuous systems, we generalize the concept of geometric phase to discrete dynamics and investigate its presence in these rotators. For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number of the system. For the discrete version of the rotated rotator considered by Berry, the rotated standard map, we further explore this connection as well as the role of the geometric phase at the onset of chaos. Further into the chaotic regime, we show that the geometric phase is also related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent. [ABSTRACT FROM AUTHOR]

An attractor of a piecewise-smooth continuous system of differential equations can bifurcate from a stable equilibrium to a more complicated invariant set when it collides with a switching manifold under parameter variation. Here numerical evidence is provided to show that this invariant set can be chaotic. The transition occurs locally (in a neighbourhood of a point) and instantaneously (for a single critical parameter value). This phenomenon is illustrated for the normal form of a boundary equilibrium bifurcation in three dimensions using parameter values adapted from of a piecewise-linear model of a chaotic electrical circuit. The variation of a secondary parameter reveals a period-doubling cascade to chaos with windows of periodicity. The dynamics is well approximated by a one-dimensional unimodal map which explains the bifurcation structure. The robustness of the attractor is also investigated by studying the influence of nonlinear terms. [ABSTRACT FROM AUTHOR]

Recurrence networks are complex networks, constructed from time series data, having several practical applications. Though their properties when constructed with the threshold value ϵ chosen at or just above the percolation threshold of the network are quite well understood, what happens as the threshold increases beyond the usual operational window is still not clear from a complex network perspective. The present Letter is focused mainly on the network properties at intermediate-to-large values of the recurrence threshold, for which no systematic study has been performed so far. We argue, with numerical support, that recurrence networks constructed from chaotic attractors with ϵ equal to the usual recurrence threshold or slightly above cannot, in general, show small-world property. However, if the threshold is further increased, the recurrence network topology initially changes to a small-world structure and finally to that of a classical random graph as the threshold approaches the size of the strange attractor. [ABSTRACT FROM AUTHOR]

A damped driven pendulum with a magnetic driving force, appearing from a solenoid, where ac current flows is considered. The solenoid acts on the magnet, which is located at a free end of the pendulum. In this system the existence and interrelation of chaos and parametric resonance is theoretically examined. Derived analytical results are supported by numerical simulations and conducted experiments. [ABSTRACT FROM AUTHOR]

We report the existence of amplitude death in a network of identical oscillators under repulsive mean coupling. Amplitude death appears in a globally coupled network of identical oscillators with instantaneous repulsive mean coupling only when the number of oscillators is more than two. We further investigate that, amplitude death may emerge even in two coupled oscillators as well as network of oscillators if we introduce delay time in the repulsive mean coupling. We have analytically derived the region of amplitude death island and find out how strength of delay controls the death regime in two coupled or a large network of coupled oscillators. We have verified our results on network of delayed Mackey–Glass systems where parameters are set in hyperchaotic regime. We have also tested our coupling approach in two paradigmatic limit cycle oscillators: Stuart–Landau and Van der Pol oscillators. [ABSTRACT FROM AUTHOR]

Advanced mathematics has analyzed complex systems, a key area of research in nonlinear sciences, including fluid mechanics, the theory of solitons, hydrodynamics, optical fibers, and chaos theory. Nonlocal integrable mKdV equations could help understand dispersive waves in nonlinear and complex media. In this manuscript, we derive bright one and two soliton solutions for a nonlocal nonlinear integrable KdV equation using an improved Hirota bilinear method (HBM). We use MATLAB to visualize the obtained results in 3D space by choosing the appropriate parameter values. It is demonstrated that these solutions have novel characteristics that differ from those of the mKdV equation. • The novel nonlocal nonlinear integrable KdV equation is considered. • The bright one and two soliton solutions for the proposed problem are presented using an improved Hirota bilinear method. • The obtained results are given in 3D figures by choosing the appropriate parameter values. [ABSTRACT FROM AUTHOR]

We investigate chaotic particle transport in magnetised plasmas with two electrostatic drift waves. Considering dissipation in the drift motion, we verify that the removed KAM surfaces originate periodic attractors with their corresponding basins of attraction. We show that the properties of the basins depend on the dissipation and the space-averaged escape time decays exponentially when the dissipation increases. We find positive finite time Lyapunov exponents in dissipative drift motion, consequently the trajectories exhibit transient chaotic transport. These features indicate how the transient plasma transport depends on the dissipation. [ABSTRACT FROM AUTHOR]

Removing the amplitude or polarity information in the feedback loop of a jerk structure shows that special nonlinearities with partial information in the variable can also lead to chaos. Some striking properties are found for this kind of hypogenetic chaotic jerk flow, including multistability of symmetric coexisting attractors from an asymmetric structure, hidden attractors with respect to equilibria but with global attraction, easy amplitude control, and phase reversal which is convenient for chaos applications. [ABSTRACT FROM AUTHOR]

A novel hybrid swarm intelligence algorithm for chaotic system parameter estimation is present. For this purpose, the parameters estimation on Lorenz systems is formulated as a multidimensional problem, and a hybrid approach based on particle swarm optimization with ant colony optimization (PSO–ACO) is implemented to solve this problem. Firstly, the performance of the proposed PSO–ACO algorithm is tested on a set of three representative benchmark functions, and the impact of the parameter settings on PSO–ACO efficiency is studied. Secondly, the parameter estimation is converted into an optimization problem on a three-dimensional Lorenz system. Numerical simulations on Lorenz model and comparisons with results obtained by other algorithms showed that PSO–ACO is a very powerful tool for parameter estimation with high accuracy and low deviations. [ABSTRACT FROM AUTHOR]

The dynamics of a point vortex moving along a straight boundary with a circular cavity subjected to a background flow is investigated. Given the constant background flow, this configuration produces regular phase portraits of the vortex motion. These phase portraits are discriminated depending on the cavity's circular shape, and then the transition to chaos of the vortex motion is investigated given an oscillating perturbation superimposed on the background flow. Based on the steady-state vortex rotation, the forcing parameters that lead to effective destabilization of vortex trajectories are distinguished. We show that, provided the cavity aperture is relatively narrow, the periodic forcing superimposed on the background flow destabilizes the vortex trajectories very slightly. On the other hand, if the cavity aperture is relatively wide, the forcing can significantly destabilize vortex trajectories causing the majority of the trajectories, which would be closed without the forcing, to move towards infinity. [ABSTRACT FROM AUTHOR]

The nonlinear and dynamic accommodating capability of time domain models makes them a useful representation of chaotic time series for analysis, modeling and prediction. This paper is devoted to the modeling and prediction of chaotic time series with hidden attractors using a nonlinear autoregressive model with exogenous inputs (NARX) based on a novel recurrent fuzzy functions (RFFs) approach. Case studies of recently introduced chaotic systems with hidden attractors plus classical chaotic systems demonstrate that the proposed modeling methodology exhibits better prediction performance from different viewpoints (short term and long term) compared to some other existing methods. [ABSTRACT FROM AUTHOR]

Nonlinear dynamics of a double pendulum rotating at a constant speed about a vertical axis passing through the top hinge is investigated. Transitions of oscillations from chaotic to quasiperiodic and back to chaotic again are observed with increasing speed of rotation. With increasing speed, a pair of new stable equilibrium states, different from the normal vertical one, appear and the quasiperiodic oscillations occur. These oscillations are first centered around the origin, but with increasing rotation speed they cover the origin and the new fixed points. At a still higher speed, more than one pair of fixed points appear and the oscillation again turns chaotic. The onset of chaos is explained in terms of internal resonance. Analytical and numerical results confirm the critical values of the speed parameter at various transitions. [ABSTRACT FROM AUTHOR]

A new coupling scheme for anticipating synchronization of chaotic systems is proposed. The scheme consists of a master system and two in series coupled slave systems with periodically switching parameters. The scheme does not require the presence of any time-delay terms either in a master or in slave systems and provides long-term anticipation. The value of anticipation time as well as the conditions of synchronization are derived in an analytical form. Analytical results are tested by numerical experiments with the chaotic Rössler and Lorenz systems as well as the Hindmarsh–Rose neuron in a regime of chaotic bursting. Also a robustness of the scheme with respect to parameter mismatch and noise is demonstrated. [ABSTRACT FROM AUTHOR]

Chaotic behavior is a common feature of nonlinear dynamics, as well as hyperchaos in high-dimensional systems. In numerical simulations of these systems it is quite difficult to distinguish one from another behavior in some situations, as the results are frequently quite “noisy”. We show that in such systems a global hyperchaotic invariant set is present giving rise to long hyperchaotic transient behaviors. This fact provides a mechanism for these noisy results. The coexistence of chaos and hyperchaos is proved via Computer-Assisted Proofs techniques. [ABSTRACT FROM AUTHOR]

In an electromagnetic standing wave formed by two super-intense colliding laser pulses, radiation reaction totally modifies the electron motion. The quantum corrections to the electron motion and the radiation reaction force can be independently small or large, depending on the laser intensity and wavelength, thus dividing the parameter space into 4 domains. The electron motion evolves to limit cycles and strange attractors when radiation reaction dominates. This creates a new framework for high energy physics experiments on the interaction of energetic charged particle beams and colliding super-intense laser pulses. [ABSTRACT FROM AUTHOR]

A dynamical phase transition from integrability to non-integrability for a family of 2-D Hamiltonian mappings whose angle, θ , diverges in the limit of vanishingly action, I , is characterised. The mappings are described by two parameters: (i) ϵ , controlling the transition from integrable ( ϵ = 0 ) to non-integrable ( ϵ ≠ 0 ); and (ii) γ , denoting the power of the action in the equation which defines the angle. We prove the average action is scaling invariant with respect to either ϵ or n and obtain a scaling law for the three critical exponents. [ABSTRACT FROM AUTHOR]

We present novel complementary relations in non-equilibrium stochastic processes. Specifically, by utilising path integral formulation, we derive statistical measures (entropy, information, and work) and investigate their dependence on variables ( x , v ), reference frames, and time. In particular, we show that the equilibrium state maximises the simultaneous information quantified by the product of the Fisher information based on x and v while minimising the simultaneous disorder/uncertainty quantified by the sum of the entropy based on x and v as well as by the product of the variances of the PDFs of x and v . We also elucidate the difference between Eulerian and Lagrangian entropy. Our theory naturally leads to Hamilton–Jacobi relation for forced-dissipative systems. [ABSTRACT FROM AUTHOR]

Properties of memristive inductorless Chua circuits are studied when they are coupled optically to characterize the oscillation quenching phenomenon of amplitude death (AD) and oscillation generation procedure of rhythmogenesis. The behaviors of these systems, when studied under coupled condition, show some new features which are not seen previously. This phenomenon is really a novel one as it is the generation of oscillation due to the interaction of two such systems each at their respective steady states. The other event is amplitude death (AD) observed by increase in the coupling strength. The numerical simulation is supported with the data obtained via analogue circuit implementation of the system. Two circuits coupled through a LED (light emitting diode) and LDR (photo resistor) pair show transition to chaotic state under parameter variation. The experimental data was collected with the help of digital to analog converter system. Our data indicates that there exist two different routes to chaos—either through period doubling or without it. [ABSTRACT FROM AUTHOR]

The solutions of Maxwell–Bloch equations in a slab of homogeneously broadened two-level atoms almost all initially inverted and prepared in a coherent state exhibit high sensitivity to initial conditions for slabs having width in narrow windows around n λ 0 / 2 ( n is an integer and λ 0 is the wavelength of the atomic transition). Sectors with two dominant modes define these windows. I compute the changes in the ratio of the forward over backward fluxes, in these sectors, as a function of the slab width and the difference in initial atomic population. [ABSTRACT FROM AUTHOR]

For a physical or biological model whose dynamics is described by a higher order difference equation u n + 1 = f ( u n , u n − 1 , … , u n − k + 1 ) , we propose a version of a target oriented control u n + 1 = c T + ( 1 − c ) f ( u n , u n − 1 , … , u n − k + 1 ) , with T ≥ 0 , c ∈ [ 0 , 1 ) . In ecological systems, the method incorporates harvesting and recruitment and for a wide class of f , allows to stabilize (locally or globally) a fixed point of f . If a point which is not a fixed point of f has to be stabilized, the target oriented control is an appropriate method for achieving this goal. As a particular case, we consider pest control applied to pest populations with delayed density-dependence. This corresponds to a proportional feedback method, which includes harvesting only, for higher order equations. [ABSTRACT FROM AUTHOR]

In this Letter we consider a three parameter unfolding of a linear degeneracy corresponding to a triple-zero eigenvalue of an equilibrium point. Using blow-up techniques we obtain a system where an exact homoclinic connection is determined. The numerical continuation of this global connection shows that it exhibits three different kinds of codimension-two degeneracies. Finally, these same codimension-two homoclinic bifurcations are detected in the Rössler system, ensuring in this way the existence of chaotic dynamics. [ABSTRACT FROM AUTHOR]

In this paper, the dynamics from the shock compacton to chaos in the nonlinearly Schrödinger equation with a source term is investigated in detail. The existence of unclosed homoclinic orbits which are not connected with the saddle point indicates that the system has a discontinuous fiber solution which is a shock compacton. We prove that the shock compacton is a weak solution. The Melnikov technique is used to detect the conditions for the occurrence from the shock compacton to chaos and further analysis of the conditions for chaos suppression. The results show that the system turns to chaos easily under external disturbances. The critical parameter values for chaos appearing are obtained analytically and numerically using the Lyapunov exponents and the bifurcation diagrams. [ABSTRACT FROM AUTHOR]

The paper examines scalar advection caused by a point–vortex pair encountering a fixed point vortex in a uniform flow. The interaction produces two types of vortex motion. First is unbounded as the pair moves unrestrictedly after encountering the fixed vortex. The scalar exchanging between the pair's bubble and fixed vortex's neighbourhood is numerically estimated. Second is bounded as the pair's vortices periodically oscillate about the fixed vortex. The pair's periodic motion perturbs scalar motion causing a portion of scalar trajectories to manifest chaotic behaviour. We analyse scalar transport using Poincaré sections, which reveal regular and chaotic transport regions. [ABSTRACT FROM AUTHOR]

We have explored some concepts of chaotic dynamics and wave light transport in foams. Using some experiments, we have obtained the main features of light intensity distribution through foams. We are proposing a model for this phenomenon, based on the combination of two processes: a diffusive process and another one derived from chaotic dynamics. We have presented a short outline of the chaotic dynamics involving light scattering in foams. We also have studied the existence of caustics from scattering of light from foams, with typical patterns observed in the light diffraction in transparent films. The nonlinear geometry of the foam structure was explored in order to create optical elements, such as hyperbolic prisms and filters. [ABSTRACT FROM AUTHOR]

Abstract: We introduce a chaos model for a permanent-magnet synchronous motor and construct a coupled chaotic motor in a complex dynamic network using the Newman–Watts small-world network algorithm. We apply adaptive pinning control theory for complex networks to obtain suitable adaptive feedback gain and the number of nodes to be pinned. Nodes of low degree are pinned to realize global asymptotic synchronization in the complex network. The proposed adaptive pinning controller is added to the complex motor network for simulation and verification. [Copyright &y& Elsevier]

Abstract: Fractional standard and sine maps are proposed by using the discrete fractional calculus. The chaos behaviors are then numerically discussed when the difference order is a fractional one. The bifurcation diagrams and the phase portraits are presented, respectively. [Copyright &y& Elsevier]

Abstract: We show that the steady states of the classical Heisenberg XXX spin-chain in an external magnetic field can be found by iterations of a quaternionic map. A restricted model, e.g., the xy spin-chain is known to have spatially chaotic steady states and the phase space occupied by these chaotic states is known to go through discrete changes as the field strength is varied. The same phenomenon is studied for the xxx spin-chain. It is seen that in this model the phase space volume varies smoothly with the external field. [Copyright &y& Elsevier]

Abstract: A four-dimensional four-parameter Chua model with cubic nonlinearity is studied applying numerical continuation and numerical solutions methods. Regarding numerical solution methods, its dynamics is characterized on Lyapunov and isoperiodic diagrams and regarding numerical continuation method, the bifurcation curves are obtained. Combining both methods the bifurcation structures of the model were obtained with the possibility to describe the shrimp-shaped domains and their endoskeletons. We study the effect of a parameter that controls the dimension of the system leading the model to present transient chaos with its corresponding basin of attraction being riddled. [Copyright &y& Elsevier]

Abstract: We propose a kind of chaotic system based on electro-optical oscillator with varying parameters, the results show that the system can enter chaos with a low gain, and can hide the delay time effectively. Furthermore, the system is more complex than the general one (with higher Lyapunov exponents and dimension). The system can achieve synchronous communication with information rate 10 Gbit/s, in 400 km optical fiber transmission distance. Furthermore, we find the system is more sensitive than the conventional system when the delay time is mismatched. [Copyright &y& Elsevier]

Abstract: In this Letter, the purity of quantum states is applied to probe chaotic dissipative dynamics. To achieve this goal, a comparative analysis of regular and chaotic regimes of nonlinear dissipative oscillator (NDO) are performed on the base of excitation number and the purity of oscillatory states. While the chaotic regime is identified in our semiclassical approach by means of strange attractors in Poincaré section and with the Lyapunov exponent, the state in the quantum regime is treated via the Wigner function. Specifically, interesting quantum purity effects that accompany the chaotic dynamics are elucidated in this Letter for NDO system driven by either: (i) a time-modulated field, or (ii) a sequence of pulses with Gaussian time-dependent envelopes. [Copyright &y& Elsevier]

Abstract: The Euler–Bernoulli kinematic model as well as the von Kármán geometric non-linearity are used to derive the PDEs governing flexible beam vibrations. The beam is embedded into a 2D temperature field, and its surface is subjected to action of the electric potential. We report how an increase of the exciting load amplitude yields the beam turbulent behavior, and how the temperature changes a scenario from a regular/laminar to spatio-temporal/turbulent dynamics. Both classical Fourier analysis and Morlet wavelets are used to monitor a strong influence of temperature on regular and chaotic beam dynamics. [Copyright &y& Elsevier]

Abstract: A modified two-dimensional lattice hydrodynamic traffic flow model is proposed by incorporating the optimal current difference effect of leading vehicles. Phase transitions and critical phenomenon are investigated near the critical point both analytically and numerically. Based on the configuration of vehicles, it is shown that two distinct jamming transitions occur: conventional jamming transition to the kink jam and jamming transition to the chaotic jam. It is shown that consideration of optimal current difference effect stabilizes the traffic flow and suppresses the traffic jam efficiently for all possible configurations of vehicles on a square lattice. [Copyright &y& Elsevier]