Chaos Behavior Research Articles

Chaos Suppression in Uncertain Generalized Lorenz–Stenflo Systems via a Single Rippling Controller with Input Nonlinearity

In this paper, a robust control design of chaos suppression is considered for generalized four-dimensional (4D) Lorenz–Stenflo systems subjected to matched/mismatched uncertainties and input nonlinearity. It is implemented by using rippling sliding mode control (SMC). A proportional-integral (PI) type scalar switching surface is designed such that the controlled dynamics in the sliding manifold becomes easy to analyze. Furthermore, only by using single rippling SMC even with input nonlinearity can we ensure the existence of the sliding mode for the controlled dynamics and suppress the chaotic behavior in a manner of rippling. Under the proposed control scheme, the chaos behavior in uncertain generalized 4D Lorenz–Stenflo systems subjected to mismatched uncertainties can be robustly suppressed to predictable bounds, which is not addressed in the literature. The numerical simulation results including matched/mismatched uncertainties and nonlinear inputs are presented to verify the robustness and validity of the rippling sliding mode controller.

Pattern generation and symbolic dynamics in a nanocontact vortex oscillator

Harnessing chaos or intrinsic nonlinear behaviours of dynamical systems is a promising avenue toward unconventional information processing technologies. In this light, spintronic devices are promising because of the inherent nonlinearity of magnetization dynamics. Here, we demonstrate experimentally the potential for chaos-based schemes using nanocontact vortex oscillators by unveiling and characterizing their waveform patterns and symbolic dynamics using time-resolved electrical measurements. We dissociate nonlinear deterministic patterns from thermal fluctuations and show that the emergence of chaos results in the unpredictable alternation of well-defined patterns. With phase-space reconstruction techniques, we perform symbolic analyses of the time series and show that the oscillator exhibits maximal entropy and complexity at the centre of its incommensurate region. This suggests that such vortex-based systems are promising nanoscale sources of entropy that could be exploited for information processing.

Hopf bifurcation, chaos control and synchronization of a chaotic fractional-order system with chaos entanglement function

This paper deals with the stability and bifurcation of equilibria in a new chaotic fractional-order system in the sense of the Caputo fractional derivative with the chaos entanglement function. We derive conditions under which the system undergoes a Hopf bifurcation and obtain critical parameter value in the Hopf bifurcation. Moreover, the linear feedback control technique is used to control and stabilize the system to equilibrium point in order to eliminate the chaotic vibration. We then design control laws to synchronize two identical chaotic fractional-order systems. Furthermore, by means of numerical simulation, we support the validity of analytical results and reveal more dynamical behaviors consisting chaos, local bifurcation, limit cycles, quasiperiodic and asymptotic stability behaviors. We further emphasize that the order of fractional derivative plays significant roles as the chaos controlling parameter and the Hopf bifurcation parameter.

Bifurcation mechanism of periodic bursting in a simple three-element-based memristive circuit with fast-slow effect

Abstract The design and analysis of simple autonomous memristive circuits are of great significance in theoretical research and practical application of complex dynamics. This paper designs a simple autonomous three-element-based memristive circuit with fast-slow effect, which is constructed by parallel connecting an active second-order memristive diode bridge with a parallel LC filter. The corresponding mathematical model is established, upon which stability analysis of the equilibrium point is performed by Routh–Hurwitz criterion. Theoretical derivation results indicate that the presented memristive circuit is always unstable, and then complex dynamical behaviors of period, chaos, quasi-period, and periodic bursting oscillation are numerically revealed through phase plane orbit, time-domain sequence, Lyapunov exponent spectrum and bifurcation diagram. In addition, bifurcation mechanisms of the periodic bursting behavior are further explored by fast-slow dynamics analysis, from which it can be found that the periodic bursting oscillation of the presented memristive circuit is a type of symmetric fold/Hopf cycle-cycle bursting oscillation. Especially, two types of dynamical behaviors of quasi-periodic oscillation and periodic bursting oscillation with a symmetric fold/Hopf cycle-cycle burster simultaneously appear in such a simple autonomous memristive circuit is amusing, which has never been reported in the previous literatures.

Organized Chaos: Daily Routines Link Household Chaos and Child Behavior Problems

The aim of this study was to examine daily routines as a potential mediator of the relation between household chaos and both child externalizing behavior and bedtime resistant behavior. Studies show that children living in chaotic households exhibit more externalizing behaviors, which when exhibited as early as the toddler and preschool years, are a risk factor for later maladjustment. Understanding the mechanisms linking household chaos to early externalizing behaviors is important since those mechanisms could be targeted as a point of intervention. Using Amazon’s Mechanical Turk (Mturk), parents (n = 120) of a child age 2–5 completed questionnaires online assessing household chaos, frequency of routines, and child behavior problems. There was a significant indirect effect of household chaos to child behavior problems through family routines (B = 0.09, SE = 0.05, CI [0.01, 0.23]) and general child routines (B = 0.15, SE = 0.06, CI [0.05, 0.31]) (independently) and an indirect effect of household chaos to bedtime resistant behavior through children’s bedtime routines (B = 0.12, SE = 0.06, CI [0.03, 0.26]). These findings suggest that household chaos and routines are distinctive constructs and that routines are a mechanism linking household chaos to early child behavior problems. Clinically, these results imply that routines may be a reasonable focus for intervention among families living in chaotic households who have young children exhibiting behavior problems.

Combined application of blockchain technology in fractional calculus model of supply chain financial system

Abstract This paper mainly studies the application of fractional calculus system in the financial system of blockchain supply chain. Firstly, based on the blockchain supply chain game model, the paper introduces the theory of fractional calculus, establishes a three-dimensional supply chain fractional calculus game model which is closer to the actual situation, and analyzes its dynamics by using the theory of nonlinear dynamics. Learning characteristics, controlling the behavior of chaos. Finally, the dissertation, distributed storage, traceability, tamper-proof and intelligent contract features of blockchain technology are applied to the bank credit system to verify the feasibility of this system.

A Jacobian approach for calculating the Lyapunov exponents of short time series using support vector regression

In order to characterize a system and to analyze the predictability of the time series under investigation, the detection of chaos and fractal behavior in experimental data is essential. In this work, support vector regression with two different kernel types namely, the linear kernel and sigmoid kernel, has been utilized for the calculation of the Lyapunov exponents of the given time series. The developed technique for the estimation of Lyapunov exponents has been validated with the help of time series generated from well known chaotic maps and also by comparing the Lyapunov exponents obtained using Rosenstein method. The results of this work reveal that the proposed technique is capable of producing accurate positive exponents for all the considered chaotic maps.

Time Delayed Feedback Control Applied in an Atomic Force Microscopy (AFM) Model in Fractional-Order

In this work, the nonlinear dynamics and control of an Atomic Force Microscopy (AFM) model in fractional-order were investigated. For analyse of the chaos behaviour, the 0–1 test was used, since this is a good tool to characterise fractional-order differential systems. To bring the system from a chaotic state to a periodic orbit, the time-delayed feedback control technique for the fractional-order systems is applied, thus controlling the chaotic behaviour. For fractional-order case, the results showed the influence of derivative order on the dynamics of the AFM system. Due to the fractional order, some phenomena comes up, which were confirmed through detailed numerical investigations by 0–1 test. The time-delayed feedback control technique was efficient to control the chaotic motion of the AFM in fractional order. In addition, the robustness of the proposed time-delayed feedback control was tested by a sensitivity analysis to parametric uncertainties.

Symmetries near the horizon

We consider a nearly-AdS2 gravity theory on the two-sided wormhole geometry. We construct three gauge-invariant operators in NAdS2 which move bulk matter relative to the dynamical boundaries. In a two-sided system, these operators satisfy an SL(2) algebra (up to non perturbative corrections). In a semiclassical limit, these generators act like SL(2) transformations of the boundary time, or conformal symmetries of the two sided boundary theory. These can be used to define an operator-state mapping. A particular large N and low temperature limit of the SYK model has precisely the same structure, and this construction of the exact generators also applies. We also discuss approximate, but simpler, constructions of the generators in the SYK model. These are closely related to the “size” operator and are connected to the maximal chaos behavior captured by out of time order correlators.

Global Stability of a Markovian Jumping Chaotic Financial System with Partially Unknown Transition Rates under Impulsive Control Involved in the Positive Interest Rate

The intrinsic instability of the financial system itself results in chaos and unpredictable economic behavior. To gain the globally asymptotic stability of the equilibrium point with a positive interest rate of the chaotic financial system, pulse control is sometimes very necessary and is employed in this paper to derive the globally exponential stability of financial system. It should be pointed out that the delayed feedback model brings an essential difficulty so that the regional control method has to be adopted. In this paper, the author firstly employs impulsive control, regional control, the Lyapunov function technique, and variational methods to derive the stochastically globally asymptotic stability criterion of the economic balance point with a positive interest rate for a delayed feedback financial system with Markovian jumping and partially unknown transition rates. Besides, the mathematical induction method and the proof by contradiction are applied synthetically to deduce the globally exponential stability of the equilibrium point with a positive interest rate for the impulsive financial system without time-delays. Moreover, numerical examples illustrate that under suitable data conditions on the two main criteria mentioned above, the interest rates are positive decimals when the financial system reaches stability, which means better economic significance.

Chaos and bifurcation behavior in a fundamental power system with electromagnetic disturbance and load disturbance

With the increasing scale of the power grid and increasingly complex structure, the power system is always affected by various disturbances and parameter changes. The power system containing electromagnetic and load power disturbance simultaneously can exhibit rich behaviors, which accords with the reality. The chaotic oscillation caused by the power disturbance may lead to unstable operation of the power grid. Therefore, a fourth-order power system model with power disturbance is established in this paper. The nonlinear characteristic of the system under multiple disturbances is studied through the bifurcation diagram, Lyapunov exponent spectrum and the phase plane. The influence of the disturbance amplitude and frequency on the system under the condition of different frequency ratio is presented through the basin of attraction with parameter mapping, and the states of different motions of the system are given more intuitively, which is helpful for better understanding the chaotic behaviors of power system.

A new six‐dimensional hyperchaotic system and its secure communication circuit implementation

SummaryIn the paper, a novel six‐dimensional hyperchaotic system is proposed for secure communication. A detailed analysis of some relevant features, such as equilibrium stability, dissipation, bifurcation, and Lyapunov exponents. The results show that there are hyperchaos, chaos, quasi‐periodic, and periodic dynamic behaviors for our constructed hyperchaotic system. Then the six‐dimensional hyperchaotic system is simulated and implemented, which verified its physical realizability. The six‐dimensional hyperchaotic system is applied to complete the signal encryption and decryption circuit design, then the circuit is tested. The results indicate that the proposed hyperchaotic system can play an important role in some key areas such as communication security and complex systems.

Longitudinal pathways linking family risk, neural risk processing, delay discounting, and adolescent substance use.

Current theories in neuroscience emphasize the crucial role of individual differences in the brain contributing to the development of risk taking during adolescence. Yet, little is known about developmental pathways through which family risk factors are related to neural processing of risk during decision making, ultimately contributing to health risk behaviors. Using a longitudinal design, we tested whether neural risk processing, as affected by family multi-risk index, predicted delay discounting and substance use. One hundred and fifty-seven adolescents (aged 13-14years at Time 1, 52% male) were assessed annually three times. Family multi-risk index was measured by socioeconomic adversity, household chaos, and family risk-taking behaviors. Delay discounting was assessed by a computerized task, substance use by questionnaire data, and risk-related neural processing by blood-oxygen-level-dependent (BOLD) responses in the amygdala during a lottery choice task. Family multi-risk index at Time 1 was related to adolescent substance use at Time 3 (after controlling for baseline substance use) indirectly through heightened amygdala sensitivity to risks and greater delay discounting. Our results elucidate the crucial role of neural risk processing in the processes linking family multi-risk index and the development of substance use. Furthermore, risk-related amygdala activation and delay discounting are important targets in the prevention and treatment of substance use among adolescents growing up in high-risk family environments.

Influence of external parameters on nonlinear behaviors in a helium dielectric-barrier discharge excited by a modulated voltage

Using a one-dimensional fluid model, period multiplication and chaos behaviors in the time domain are numerically investigated in atmospheric pressure helium dielectric-barrier discharge excited by a modulated sinusoidal voltage. The results indicate that with the increasing duty ratio of the modulated voltage, various nonlinear behaviors are obtained, including asymmetric single-period, period-three, period-seven, chaotic, and symmetric single-period states. More details are revealed that period-four, period-nine, and period-thirteen states can also be observed between period-three and period-seven states. For the period-three state, there are six current pulses in each current period, which have different amplitudes with each other. Besides the duty ratio, the sinusoidal frequency of the modulated voltage is varied, which results in similar nonlinear behaviors. Additionally, under a duty ratio of 80%, it maintains a stable period-two state with the increasing voltage amplitude or the decreasing gap width. During this process, the pulse number and duration time increase per half voltage cycle. Finally, spatial distributions of the electric field, electron density, and ion density are investigated for the novel period-three state, which is qualitatively explained through analyzing the influence of the averaged density of electrons and metastable states just before the discharge moments.

A simple Jerk-like system without equilibrium: Asymmetric coexisting hidden attractors, bursting oscillation and double full Feigenbaum remerging trees

Abstract The topic associated with hidden attractor and multistability has been received considerable attention recently. In this paper, a novel no-equilibrium Jerk-like chaotic system is constructed and explored. Particularly, owing to the absence of the equilibria, such a new system can be categorized as a system with hidden attractors. More interestingly, this system holds three conspicuous characteristics. The first one is that various asymmetric coexisting hidden attractors and complicated transient chaos behaviors are obtained. The second one is the new finding of the periodic bursting oscillation and unusual phenomenon of transient periodic bursting oscillation in the system. The third one is the observation of the amazing and rare phenomenon of one to two full Feigenbaum remerging trees, namely, antimonotonicity. To the best knowledge of us, the last two special features are first discovered and have never been reported, especially in such no-equilibrium chaotic system that exhibits hidden attractors. With the help of phase portraits, time series, bifurcation diagram, Lyapunov exponents, chaotic dynamical diagram, basin of attraction and so forth, the rich hidden dynamical properties of this system are systematically analyzed and investigated. Additionally, a hardware electronic circuit on a breadboard is carried out. A very good similarity between the hardware experimental results and the theoretical analysis testifies the feasibility and practicality of this original system.

Chaos Behavior in Group Formation

Chaos Behavior in Group Formation

Complex Dynamical Behaviors of a Fractional‐Order System Based on a Locally Active Memristor

A fractional‐order locally active memristor is proposed in this paper. When driven by a bipolar periodic signal, the generated hysteresis loop with two intersections is pinched at the origin. The area of the hysteresis loop changes with the fractional order. Based on the fractional‐order locally active memristor, a fractional‐order memristive system is constructed. The stability analysis is carried out and the stability conditions for three equilibria are listed. The expression of the fractional order related to Hopf bifurcation is given. The complex dynamical behaviors of Hopf bifurcation, period‐doubling bifurcation, bistability and chaos are shown numerically. Furthermore, the bistability behaviors of the different fractional order are validated by the attraction basins in the initial value plane. As an alternative to validating our results, the fractional‐order memristive system is implemented by utilizing Simulink of MATLAB. The research results clarify that the complex dynamical behaviors are attributed to two facts: one is the fractional order that affects the stability of the equilibria, and the other is the local activeness of the fractional‐order memristor.

Nonlinear analysis of the locomotive traction system with rub-impact and nonlinear stiffness

Considering rub-impact forces, eccentricity of rotor, and nonlinear stiffness of armature shaft, a dynamic differential equation is built to investigate the bifurcation and chaos behavior of the locomotive traction system. The nonlinear analysis methods are inclusive of bifurcation diagrams, phase plane portraits, Poincaré maps, displacement–time curves, and spectrograms. The simulation results reveal the complex dynamic comprising period-3 to quasi-periodic bifurcation and intermittent bifurcation. Some research results are references for dynamic design and rub-impact fault diagnosis of the locomotive traction system.

BOVESPA: Stochastic or Deterministic?

Abstract We aim to present an interdisciplinary way of showing the subject determinism versus stochasticity; and write the text in such a way that this subject can be treated from the point of view of physics teaching. We approach the technical part of this work intuitively and later we present this question in a more formal way. When the trajectory of a dynamical system in the phase space repeats itself after some time. We say that the system displays recurrence. Recurrence plots (RP) and recurrence quantification analysis (RQA) took place as tools to investigate this property. We employ the RP and the RQA the behavior of a long time series of the returns of the Bovespa index. We have carefully studied the obtention of the parameters for the phase space reconstruction of the supposed dynamical system which created the time series. After building the RPs for the time series of the returns, the values of the quantities from RQA were computed and then compared with values obtained for the randomized series. Our investigations suggest that the real financial market dynamics is a combination of deterministic chaos and stochastic behavior.

Self-regulation mitigates the association between household chaos and children's behavior problems

Given the potential negative effects that early childhood behavioral problems have on later development, it is important to elucidate risk and protective factors. This study examined household chaos as a predictor of externalizing and internalizing problems among young children from low-income families. Additionally, self-regulation was examined as a moderator of the association between chaos and behavior problems. One hundred young adult mother-toddler dyads participated. Moderation analyses indicated that self-regulation buffered the association between household chaos and child behavior problems. Specifically, greater household chaos was associated with more behavior problems, but only among children with poorer self-regulation. Notably, this pattern was observed for both externalizing and internalizing problems. These findings suggest that early interventions targeting young children's self-regulation skills could help prevent behavior problems among children living in chaotic home environments.