Chaos Control Research Articles

Decoupled reliability-based design optimization with a double-step modified adaptive chaos control approach

Decoupled reliability-based design optimization with a double-step modified adaptive chaos control approach

A Fractional-Order Discrete Lorenz Map

In this paper, a discrete Lorenz map with the fractional difference is analyzed. Bifurcations of the map in commensurate-order and incommensurate-order cases are studied when an order and a parameter are varied. Hopf bifurcation and periodic-doubling cascade are found by the numerical simulations. The parameter values of Hopf bifurcation points are determined when the order is taken as a different value. It can be concluded that the parameter decreases as the order increases. Chaos control and synchronization for the fractional-order discrete Lorenz map are studied through designing the suitable controllers. The effectiveness of the controllers is illustrated by numerical simulations.

Stabilization of Stochastic Exchange Rate Dynamics Under Central Bank Intervention Using Neuronets

The exchange rate dynamics affect national economies because fluctuations in currency prices distort their economic activity. To maintain an optimal exchange rate policy, these dynamics are crucial for countries with a trade economy. Due to the difficulty in predicting the participants behavior in some complex economic systems, which might throw the system into chaos, a novel stochastic exchange rate dynamics (SERD) model is introduced and investigated in this paper. Furthermore, a neural network approach is proposed and examined as a control chaos method to address the problem of stabilizing SERD through central bank interventions. Derived from power activation feed-forward neuronets, a 2-input weights-and-structure-determination-based neuronet (2I-WASDBN) model for controlling chaos in SERD under central bank intervention is presented in this paper. Six simulation experiments on stabilizing the chaotic behavior of the SERD model show that the 2I-WASDBN model outperforms other well-performing neural network models and that it is more effective than traditional methods for controlling chaos. By examining the volume of necessary intervention predicted by the 2I-WASDBN model, central banks can better comprehend exchange rate fluctuations and, in conjunction with their monetary policies, can make more precise decisions regarding the strategy of their interventions.

Investigation of complex dynamics and chaos control of the duopoly supply chain under the mixed carbon policy

Against the background of the mixed carbon policy (carbon tax‑carbon trading) implemented in China, the authors analyze the complexity of a series of competition decisions between supply chains through constructing Cournot(Duopoly)game model between supply chains. The dynamics of the proposed game model and the time evolution of the supply chains are described by a nonlinear discrete dynamical system. The equilibrium point of the discrete dynamical system is obtained and its local stability is discussed. The stability of the equilibrium point is further discussed by numerical simulation, which is affected by the speed of adjusting parameters and some other cost parameters. Finally, we apply the delayed feedback control method to suppress and overcome the chaos of the discrete dynamical system. It can effectively promote the discrete dynamical system to return to the stable behavior. It is hoped that the current research can provide a theoretical basis for the competitive decision-making of supply chain node enterprises.

Controlling of periodicity and chaos in a three dimensional prey predator model introducing the memory effect

In an ecological system, omnivores are often significantly important as they feed upon more than one trophic level in a food chain model. Intraguild predation is a special kind of omnivory that is ubiquitous in many ecological communities. A lot of field experiments suggest that the experience over a time duration in the recent past affects the growth rate of all species at the present time. Here, we have considered the Caputo type fractional ordered three-species food chain model. The memory effect is explained in terms of the order of the fractional derivative. Intermediate, top predators feed upon prey by Holling type I functional response and the top predator consumes intermediate predator by Holling type II functional response. Here, we established the existence and uniqueness of the solution of the considered system. Also, we prove the positivity and boundedness of the system solution. All possible feasible equilibrium points with required parametric conditions are discussed in the text. The local stability of all feasible equilibrium points and the parametric conditions of global stability of all non-trivial equilibrium points are discussed. The memory effect can stabilize the system from the periodic oscillatory situation which has been proved through the Hopf bifurcation analysis. Finally, some numerical simulation has been carried out to make significant comments on the dynamics of the considered system about the memory effect and other system parameters. It is clear from the numerical simulations that the order of fractional derivative can be taken as the indicator of chaos control. The biological interpretations make the article most significant from the ecological point of view.

Stability, bifurcation analysis, and chaos control of a discrete bioeconomic model

In this paper, we propose a host‐parasitoid model with harvest effort. The existence and stability of a positive fixed point are analyzed. The period‐doubling and Neimark–Sacker bifurcations are studied. These analyses are achieved by applying the normal form of the difference‐algebraic system, bifurcation theory, and center manifold theorem. Furthermore, we apply a state‐delayed feedback control strategy to control the complex dynamics of the proposed model. Numerical examples and simulations are given to verify our findings. Owing to the framework of Nicholson–Bailey host‐parasitoid system, the proposed difference‐algebraic model shows rich dynamics compared with the continuous‐time models.

Chaotic convection in a magnetic fluid in rotation subjected to a pseudo-vector type force

This paper reports the chaos control on the convection in a magnetic fluid in rotation subjected to a pseudo-vector type force. We performed a truncated Galerkin expansion which allowed to describe the system by a Lorenz-type model. We characterized the dynamical system by plotting bifurcation diagrams, Lyapunov exponents and phase spaces. It is found that the system exhibits rich behaviors depending on the variation of the system parameters. Finally, we noticed that the chaotic domain is considerably reduced with the increase of the helical force whereas the Taylor number enlarges it.

Error Propensities Amongst Finance and Accounting Professionals: Can We Quantitatively Measure Illusion of Control or Chaos?

Most financial and accounting tasks and analytics, whether associated with the past or future, assume knowledge of process, variation, and statistics. Yet, finance and accounting personnel averaging 13 years of experience could not distinguish non-random from random time-series strings in an assessment using statistical process control charts. Respondents scored no better than guessing compared to a series of true-false questions. Latent class analysis methods within partial least square structural equation modeling successfully uncovered segments of respondents with large explained variance and significant paths to explicate tendencies toward type I or type II error rates, i.e., an illusion of control or illusion of chaos. Relationships between the desirability of control, personal fear of invalidity, and error rates were more varied than expected.

Stability, Bifurcation, and Chaos Control of Two-Sided Market Competition

Benefitting from the popular uses of internet technologies, two-sided market has been playing an increasing prominent role in modern times. Users and developers can interact with each other through two-sided platforms. The two-sided market structure has been investigated profoundly. Through building a dynamics two-sided market model with bounded rational, stability conditions of the two-sided market competition system are presented. With the help of bifurcation diagram, Lyapunov exponent, and strange attractor, the stability of the two-sided market competition model is simulated. At last, we use the time-delayed feedback control (TDFC) method to control the chaos. Our main results are as follows: (1) when the adjustment speed of two-sided increases, the system becomes bifurcation, and chaos state happens finally. When the system is stable, the consumer fee is positive while developer fee is negative. (2) When the user externality increases, the stable area of the system increases, and the difference in user externality leads the whole system more stable. When the system is stable, the developer fee decreases. (3) The stable area becomes larger when developer externality increases; when the system is stable, the user fee becomes lower and developer fee becomes higher when developer externality increases. (4) The TDFC method is presented for controlling the chaos; we find that the system becomes more stable under the TDFC method.

Qualitative behavior of a discrete predator–prey system under fear effects

Abstract Numerous field data and experiments on the perching birds or songbirds show that the fear of predators can cause significant changes in the prey population. Fear of predatory populations increases the chances of survival of the prey population, and this can greatly reduce the reproduction of the prey population. The influence of fear has contributed a leading role in both the environmental biology and theoretical ecology. Taking into account the interaction of predator–prey with non-overlapping generations, a discrete-time model is proposed and studied. Keeping in mind the biological feasibility of species, the existence of fixed points is studied along with the local asymptotic behavior of the proposed model around these fixed points. Furthermore, taking into account the oscillatory behavior of the model, various types of bifurcations are analyzed about biologically feasible fixed points with an application of center manifold theory and bifurcation theory of normal forms. Existence of chaos is discussed, and fluctuating and chaotic behavior of the system is controlled through implementation of different chaos control procedures. The illustration of theoretical discussion is carried out via validation of observed experimental field data and appropriate numerical simulation.

Bifurcations and chaos control in a discrete-time prey–predator model with Holling type-II functional response and prey refuge

In this paper, we study the complex dynamical behavior in a discrete prey–predator model with Holling type II functional response with prey refuge. It is exhibited that the system shows different types of bifurcations viz. flip bifurcation, transcritical bifurcation and Neimark–Sacker bifurcation(NSB) by using center manifold theorem and bifurcation theory. Moreover, the chaos occurred in the system has been controlled by deploying control strategies viz. state feedback, pole placement and hybrid control techniques. The certain conditions have been determined under which chaos and bifurcation can be stabilized. The extensive numerical simulation is performed to demonstrate the analytical findings.

Optimal pricing and complex analysis for low-carbon apparel supply chains

Motivated by the low-carbon economic development, we study the competition issues in apparel supply chains considering consumers’ low-carbon preferences. In this paper, we construct static and dynamic decision-making models under different game scenarios based on the centralized and decentralized frameworks. Firstly, we explore the critical conversion conditions between the centralized and decentralized frameworks with the static game models. The centralized model benefits the whole supply chain when the low-carbon investment coefficient is moderate. On the contrary, the decentralized model benefits the supply chain when the low-carbon investment coefficient is smaller or larger. Secondly, combined with the local and global bifurcation theory, we examine the complex effect of adjustment parameters on the dynamic system. The dynamic game systems show bifurcation, chaos, and multi-stability as the adjustment parameters change continuously. Therefore, we apply a hybrid chaos control method to stabilize the dynamic system. Thirdly, we compare the average profits in the dynamic game scenarios and show the complex relationships with the varying parameters. Finally, some management insights and suggestions are presented based on our findings.

Chaos and Dynamics Induced by the Amplitude of Load Torque: Analysis and Control

In this contribution, the dynamics and chaos control of a permanent magnet reluctance synchronous motor (PMSM) with constant, sinusoidal, and square load torque taking the reference rotor speed and the stator voltage on d-q-axis are analyzed. The analysis shows that under some conditions, varying amplitude of the load torque, PMSM presents period doubling route to chaos with one and double-scroll attractors and bursting oscillations. We use the self-feedback delay controller to stabilize the output trajectory by forcing to the periodic solution. Furthermore, an analog circuit is designed and implemented in OrCAD-PSpice software to verify the numerical results and good agreement is observed with numerical results.

Parameter Identification for Memristive Chaotic System Using Modified Sparrow Search Algorithm

A memristor is a non-linear element. The chaotic system constructed by it can improve its unpredictability and complexity. Parameter identification of a memristive chaotic system is the primary task to implement chaos control and synchronization. To identify the unknown parameters accurately and quickly, we introduce the Sine Pareto Sparrow Search Algorithm (SPSSA), a modified sparrow search algorithm (SSA). in this research. Firstly, we introduce the Pareto distribution to alter the scroungers’ location in the SSA. Secondly, we use a sine-cosine strategy to improve the producers’ position update. These measures can effectively accelerate the convergence speed and avoid local optimization. Thirdly, the SPSSA is used to identify the parameters of a memristive chaotic system. The proposed SPSSA exceeds the classic SSA, particle swarm optimization algorithm (PSO), and artificial bee colony algorithm (ABC) in simulations based on the five benchmark functions. The simulation results of parameter identification of a memristive chaotic system show that the method is feasible, and the algorithm has a fast convergence speed and high estimation accuracy.

Chaotic microlasers caused by internal mode interaction for random number generation

Chaotic semiconductor lasers have been widely investigated for generating unpredictable random numbers, especially for lasers with external optical feedback. Nevertheless, chaotic lasers under external feedback are hindered by external feedback loop time, which causes correlation peaks for chaotic output. Here, we demonstrate the first self-chaotic microlaser based on internal mode interaction for a dual-mode microcavity laser, and realize random number generation using the self-chaotic laser output. By adjusting mode frequency interval close to the intrinsic relaxation oscillation frequency, nonlinear dynamics including self-chaos and period-oscillations are predicted and realized numerically and experimentally due to internal mode interaction. The internal mode interaction and corresponding carrier spatial oscillations pave the way of mode engineering for nonlinear dynamics in a solitary laser. Our findings provide a novel and easy method to create controllable and robust optical chaos for high-speed random number generation.

Control of Multistability and Chaos in a Thin Magnetostrictive Actuator Model with Quintic Nonlinearity

Control of Multistability and Chaos in a Thin Magnetostrictive Actuator Model with Quintic Nonlinearity

Chaos control and characterization of brushless DC motor via integral and differential fractal-fractional techniques

ABSTRACT Although brushless DC motors have been preferably used in wide industrial applications on the basis of superior properties and stable operation, the stability of brushless DC motors is found to be dependent on their chaotic characteristics and initial operating conditions. Owing to such characteristics, this article presents the chaos control and chaotic characteristics of brushless DC motors through newly defined mathematical techniques, so-called fractal-fractional differentiations. Mathematical modeling of the governing equations of the brushless DC motor has been developed by means of Caputo, Caputo-Fabrizio and Atangana-Baleanu fractal-fractional differential operators. The sensitive initial conditions and vibrant parameters have been analyzed for the comparative performance and assessment of the brushless DC motor. The numerical simulations of fractal-fractionalized governing equations of the brushless DC motor have been performed by means of the Adams-Bashforth-Moulton method using MATLAB package. Finally, the graphical illustrations have been underlined for the proposed Caputo, Caputo-Fabrizio and Atangana-Baleanu fractal-fractional differential operators subject to the chaotic behaviors investigated for the brushless DC motor.

In the presence of fear and refuge: Permanence, bifurcation and chaos control of a discrete-time ecological system

In this paper, we aim to study the effects of fear of predation in the presence of a competitor species and availability of refuge for the prey population. A discrete-time model of prey–predator–competitor type is formulated to study the dynamical relationship between the interacting species by deriving the conditions for local stability, permanence and existence of Neimark–Sacker bifurcation. A hybrid control technique based on state feedback strategy is implemented to control the chaos in the system. Finally, some numerical simulations are carried out to illustrate the theoretical discussions.

Computational chaos control based on small perturbations for complex spectra simulation

In this paper, we propose to use a computational method of chaos control to simulate complex experimental spectra. This computational chaos control technique is based on the Ott–Grebogi–York (OGY) method. We chose the logistic map as the base mathematical model for the development of our work. For the numeric part, we created arbitrary precision algorithms to generate the solutions. This way, we completely eliminated any degradation of chaos from our results. These algorithms were also necessary for the proper perturbation process that the computational chaos control method requires. We control the chaos of the logistic map in two cases of Period 1 and one case of Period 2 to demonstrate that our control method works. The behavior of a complex experimental spectrum was taken and numerically simulated. The simulated spectrum was obtained by controlling the chaos of the logistic map in a variable way with the methods proposed in this work. Our results show that it is possible to simulate very complicated experimental spectra by computationally controlling the chaos of an equation unrelated to the experimental system.

Is fractional-order chaos theory the new tool to model chaotic pandemics as Covid-19?

The deadly outbreak of the second wave of Covid-19, especially in worst hit lower-middle-income countries like India, and the drastic rise of another growing epidemic of Mucormycosis, call for an efficient mathematical tool to model pandemics, analyse their course of outbreak and help in adopting quicker control strategies to converge to an infection-free equilibrium. This review paper on prominent pandemics reveals that their dispersion is chaotic in nature having long-range memory effects and features which the existing integer-order models fail to capture. This paper thus puts forward the use of fractional-order (FO) chaos theory that has memory capacity and hereditary properties, as a potential tool to model the pandemics with more accuracy and closeness to their real physical dynamics. We investigate eight FO models of Bombay plague, Cancer and Covid-19 pandemics through phase portraits, time series, Lyapunov exponents and bifurcation analysis. FO controllers (FOCs) on the concepts of fuzzy logic, adaptive sliding mode and active backstepping control are designed to stabilise chaos. Also, FOCs based on adaptive sliding mode and active backstepping synchronisation are designed to synchronise a chaotic epidemic with a non-chaotic one, to mitigate the unpredictability due to chaos during transmission. It is found that severity and complexity of the models increase as the memory fades, indicating that FO can be used as a crucial parameter to analyse the progression of a pandemic. To sum it up, this paper will help researchers to have an overview of using fractional calculus in modelling pandemics more precisely and also to approximate, choose, stabilise and synchronise the chaos control parameter that will eliminate the extreme sensitivity and irregularity of the models.