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The current study is concerned with the dynamical investigation, synchronization, and engineering application of a new variable-order fractional neural network. The model of the variable-order fractional neural network is presented, and its chaotic behavior is studied through well-known dynamical tools. Then, a new control technique is proposed for the control of the system. Although finite-time estimators considerably enhance the performance of controllers, studies that offer finite-time estimators for the control of fractional-order systems are rare in the literature. Motivated by this, as a novel approach, the proposed control technique is equipped with a finite-time estimator, which is able to approximate highly nonlinear disturbances and uncertainties. The stability and finite-time convergence of the sliding surface and error dynamics based on the proposed control technique are proven. Through numerical simulations, the effectiveness of the designed control scheme in the presence of complex time-varying disturbances is illustrated. Then, a voice encryption application has been implemented in order to show the feasibility of data security applications of the proposed variable-order neural network. Finally, to investigate the effectiveness of the implemented data security application, the entropy values for original, encrypted, and decrypted voice data are presented. Numerical analyses of encryption clearly confirm that encryption is done securely and there is no corruption or data loss in encryption and decryption processes. [ABSTRACT FROM AUTHOR]

In this article, a fixed-time adaptive fault-tolerant control approach is presented for the attitude tracking of rigid spacecraft subject to inertia uncertainties, external disturbances, and actuator faults. The designed controller is developed as a combination of the fixed-time integral sliding mode control and parametric adaptation technique. The fixed-time integral sliding mode controller has no singularity problem naturally by constructing a novel integral sliding mode surface based on the bi-limit homogeneous method. Moreover, the parametric adaptation technique is incorporated to estimate the total uncertainty indirectly. Benefiting from this development, the designed controller is smooth with no obvious chattering phenomenon and does not require any information on the upper bound of the total uncertainty. The attitude and angular velocity tracking errors under the designed controller can regulate to the minor fields about zero in fixed time. A remarkable feature of the designed controller is that it is not only robust against inertia uncertainties and external disturbances, but also insensitive to multiple types of actuator faults. Finally, simulation results show the effectiveness and merits of the presented control approach. • Fixed-time adaptive fault-tolerant control approach for attitude tracking of rigid spacecraft. • Combination of fixed-time integral sliding mode control and parametric adaptation technique. • Novel integral sliding mode surface based on bi-limit homogeneous method eliminates singularity problem. • Smooth controller with no chattering phenomenon, regulates tracking errors to minor fields around zero in fixed time. • Robust against inertia uncertainties and external disturbances. [ABSTRACT FROM AUTHOR]

Despite the existence of promising methods for controlling complex systems, there is still a need for further advancement in controlling and synchronizing fractional systems. This is even more monumental when it comes to practical applications with faults and physical constraints present in their control actuators. To address this issue, the current study proposes a new control technique that utilizes a recurrent neural network-based finite-time super-twisting algorithm for fractional-order systems. The proposed controller is enhanced with an intelligent observer to account for faults and limitations that may be present in the control actuator of the fractional-order systems. The proposed method allows the system to be regulated even in the presence of control input constraints and faults. Moreover, the proposed technique guarantees that the closed-loop system will converge in a finite amount of time. The control design is explained in detail, and its finite-time stability is proven. To evaluate the performance of the controller, we applied it to two different fractional-order systems that were subject to control input limitations and faults. The outcomes of the proposed approach were then compared with those obtained using a state-of-the-art technique for fractional-order systems to further validate the effectiveness of our proposed approach. • A controller proposed for fractional systems using recurrent neural network-based finite-time super-twisting algorithm. • Controller enhanced with intelligent observer to handle faults and limitations in control actuators. • Proposed method enables system regulation despite control input constraints and faults. • Guaranteed finite-time convergence of closed-loop system. • Performance evaluated on two fractional-order systems, outperforming state-of-the-art techniques. [ABSTRACT FROM AUTHOR]

• We develop a new finite-time method for controlling and synchronising fractional-order financial systems • A Deep Learning Recurrent Neural Network is integrated by terminal sliding mode control • The proposed technique is applied to a chaotic fractional-order financial model with market confidence under highly complex and time-varying uncertainties • It is shown comparatively that when the disturbances are high, the conventional TSMC methods fail Disturbances are inevitably found in almost every system and, if not rejected, they could jeopardize the effectiveness of control methods. Thereby, employing state-of-the-art observers could improve the reliability and performance of controllers dramatically. Motivated by this, we develop a new finite-time method for controlling and synchronising fractional-order systems. The deep learning recurrent neural network, which is a strong tool in handling highly complex and time-varying uncertainties, is integrated by terminal sliding mode control. On the basis of Lyapunov stability theorem, the finite-time convergence and stability of the closed-loop system are proven. Then, the proposed technique is applied to a chaotic fractional-order financial model with market confidence. In simulations, it is supposed that the system is operating in the presence of complex disturbances. The results of the proposed technique are compared with terminal sliding mode control. Numerical results illustratively confirm the theoretical claims about the robust performance of the deep learning control technique. Also, it is shown that when the disturbances are high, the conventional methods fail. [ABSTRACT FROM AUTHOR]

• In our novel approach, H ∞ attenuates the effect of uncertainties and through H 2 the consumed control energy is minimized • No attempt so far has been made to design this type of controller for chaotic financial systems • Applying optimal mixed H 2 / H ∞ control, exploits the positive features of both controllers for financial markets • A hyperchaotic financial system with coexisting attractors is investigated • Numerical simulations clearly confirm the effectiveness of the new model Due to the importance of consumed control energy in financial systems, employing an optimal controller for these systems could be beneficial. Also, the presence of disturbances is undeniable in most of these systems. Hence, applying optimal mixed H 2 / H ∞ control, which posses the positive features of both H ∞ and H 2 control, could bring up luminous results for these systems. However, in the literature, no attempt has been made to design this type of controller for chaotic financial systems. This issue motivated the current study. In this study, we present a type-2 fuzzy-based optimal mixed H 2 / H ∞ control for a hyperchaotic financial system. In this approach, H ∞ attenuates the effect of uncertainties and through H 2 the consumed control energy is minimized. Also, since the proposed controller is equipped with a type-2 fuzzy observer, it can easily handle uncertainties and unknown functions. Via Lyapunov theorem, it is confirmed that all signals in the system are bounded. In the numerical simulation, firstly, a hyperchaotic financial system with coexisting attractors is investigated. The proposed controller is then applied to the financial system, and the proposed technique's performance is assessed. Numerical simulations clearly confirm the theoretical claims about the effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]

The identification of influential nodes in complex networks has been a topic of immense interest. In most cases, the local approach represented by degree centrality performs well but has limitations when dealing with the bridge nodes. In order to solve the problem of being trapped in the locality, researchers have proposed many useful methods. The gravity model is an emerging research direction among them. However, such models have to exhaust the shortest distance between all nodes, which renders them impractical and difficult to run over large graphs. In order to address this issue, we propose a random walk-based gravity model to identify influential spreaders. Our proposed model decreases the time complexity of calculating the shortest distance—a critical step in the conventional gravity models, from O (| V | 2) to O (| V | * γ * l r (l - r)) , and reduces space complexity of O (| V | 2) to O (< K > 2 | V |) , where < K > 2 ≪ | V | and γ * l r (l - r) ≪ | V |. Some random walk properties are also investigated to support our model. In order to demonstrate the feasibility of the proposed gravity centrality, we have verified its spreading ability and convergence speed under different random walk strategies. Experimental results indicate that our method performs far better than most gravity models. [ABSTRACT FROM AUTHOR]

The neighboring coordinates are strongly correlated in 3D images, but the encryption format of 3D images is not suitable for 2D image encryption. Thus, a novel compatible chaotic image encryption system based on checkers rules and shift register is proposed in this paper. Firstly, a discrete memristive hyperchaotic map(a discrete hyperchaotic map coupled with a memristor) is used to generate the chaotic sequence of the cryptosystem. The hyperchaotic map is analyzed through Phase diagrams, Lyapunov exponent spectrum(LEs), and bifurcation diagram. Secondly, the data format of a 3D image is converted to a 2D image data format. Then, the checkers rules are used to scramble the 2D image data format. Finally, the scrambled data and the chaotic sequence are converted to character types, and the scrambled data is further encrypted by the shift register principle. The 2D image and 3D image are tested and the results show that the compatibility encryption system has good performance, significantly reducing the correlation among the data. [ABSTRACT FROM AUTHOR]

In the present paper, for the first time, we propose a variable-order hyperchaotic system for information security. Firstly, we study the dynamical behaviors of a memristor oscillator through well-known numerical and analytical tools, such as the Lyapunov exponents, stability of equilibria, and bifurcation diagram. Then as an engineering application, a variable-order fractional version of the system is proposed for sound encryption. In comparison with integer and conventional constant fractional-order chaotic memristor oscillator, the proposed variable-order fractional system shows more complex characteristics and more degrees of freedom due to the existence of time-varying fractional derivatives. Thus, the proposed system is an appropriate choice for data transmission and information security. To illustrate the proper performance of the suggested system for encryption purposes, sound encryption is successfully performed, and its excellent results are demonstrated. The predictor-corrector method is utilized for numerical simulation. Then, a new type-2 fuzzy disturbance observer-based robust control is offered for synchronization of the variable-order hyperchaotic system. The stability and convergence of the disturbance estimator and closed-loop system are proven. Lastly, the synchronization results, which confirm the appropriate performance of the proposed method in the presence of the external disturbances, are demonstrated. [ABSTRACT FROM AUTHOR]

• We have developed a model for complex economic systems utilizing variable-order fractional derivatives. • The system's behaviour is highy dependent upon the value of fractional-order derivatives. • A nonlinear model predictive controller (NMPC) for hyperchaotic control is introduced. • The robust control suppresses the chaotic behaviour and stabilizes the close-loop system, while also rejecting any external bounded disturbances. Mathematical modelling plays an indispensable role in our understanding of systems and phenomena. However, most mathematical models formulated for systems either have an integer order derivate or posses constant fractional-order derivative. Hence, their performance significantly deteriorates in some conditions. For the first time in the current paper, we develop a model of an economic system with variable-order fractional derivatives. Our underlying assumption is that the values of fractional derivatives are time-varying functions instead of constant parameters. The effects of variable-order time derivative into the economic system is studied. The dependency of the system's behaviour on the value of the fractional-order derivative is investigated. Afterwards, a nonlinear model predictive controller (NMPC) for hyperchaotic control of the system is suggested. The necessary optimality and sufficient conditions for solving the nonlinear optimal control problem (NOCP) of the NMPC in the form of fractional calculus with variable-order which is formulated as a two-point boundary value problem (TPBVP) are derived. Since the proposed methodology is a robust controller, the efficiency of the proposed controller in the presence of external bounded disturbances is examined. Simulation results show that not only does the presented control approach suppresses the related chaotic behaviour and stabilizes the close-loop system, but it also rejects the external bounded disturbances. [ABSTRACT FROM AUTHOR]

• Spectral entropy and spectral Min-Entropy are computed, and the phenomenon of multi-stability is shown. • A new chattering-free robust sliding mode controller with a neural network observer is proposed. • Based on the Lyapunov stability theorem, the asymptotical stability of the closed-loop system is confirmed. • Numerical results demonstrate the chattering-free and effective performance of the proposed control method. An immense body of research has focused on chaotic systems, mainly because of their interesting applications in a wide variety of fields. A comprehensive understanding and synchronization of chaotic systems play pivotal roles in practical applications. To this end, the present study investigates a multi-stable fractional-order chaotic system. Firstly, some dynamical features of the system are described, and the chaotic behaviour of the system is verified. Then, both spectral entropy and spectral Min-Entropy are computed, and the phenomenon of multi-stability is shown. Besides, the combination of a new chattering-free robust sliding mode controller with a neural network observer is proposed for the synchronization of the fractional-order system. With the neural network estimator, unknown functions of the system are obtained, and the effects of disturbances are completely taken into account. Also, based on the Lyapunov stability theorem, the asymptotical stability of the closed-loop system is confirmed. Lastly, the proposed control technique is applied to the fractional-order system. Numerical results demonstrate the chattering-free and effective performance of the proposed control method for uncertain systems in the presence of unknown time-varying external disturbances. [ABSTRACT FROM AUTHOR]

• To best knowledge of authors, the first work introducing variable memory indexes in a SIRD epidemic model to estimate the COVID-19. • Fractional-order SIRD model with incommensurate fractional-orders defined by a time-dependent function contrary a constant. • Identification of a universality in the COVID-19 evolution among geographical regions. COVID-19 is a novel coronavirus affecting all the world since December last year. Up to date, the spread of the outbreak continues to complicate our lives, and therefore, several research efforts from many scientific areas are proposed. Among them, mathematical models are an excellent way to understand and predict the epidemic outbreaks evolution to some extent. Due to the COVID-19 may be modeled as a non-Markovian process that follows power-law scaling features, we present a fractional-order SIRD (Susceptible-Infected-Recovered-Dead) model based on the Caputo derivative for incorporating the memory effects (long and short) in the outbreak progress. Additionally, we analyze the experimental time series of 23 countries using fractal formalism. Like previous works, we identify that the COVID-19 evolution shows various power-law exponents (no just a single one) and share some universality among geographical regions. Hence, we incorporate numerous memory indexes in the proposed model, i.e., distinct fractional-orders defined by a time-dependent function that permits us to set specific memory contributions during the evolution. This allows controlling the memory effects of more early states, e.g., before and after a quarantine decree, which could be less relevant than the contribution of more recent ones on the current state of the SIRD system. We also prove our model with Italy's real data from the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University. [ABSTRACT FROM AUTHOR]

Nowadays, chaotic systems are attracting considerable attention due to their special features. The aim of this paper is to study a four-dimensional system that lacks any equilibria. Also, this non-equilibrium system has hidden attractors. Dynamical behaviors of the system have been investigated using well-known numerical simulations and analyses such as phase portraits, Poincaré maps, Lyapunov exponents, bifurcation diagrams, and basins of attraction. This way, the chaotic behavior in the system is verified. In addition, the chaotic behavior of the system has been studied by designing and implementing a real-time analog circuit. The circuitry implementation of the system is presented, and the dynamical behaviors of the system have been empirically demonstrated. To characterize the circuit an automatic routine through LabView has been developed in which by increasing a parameter of the system the bifurcation diagram has been obtained and depicted. A DAQ 6363 storing temporal series of one second to posteriory has been used to acquire the data and analyze such information. Experimental results clearly illustrate the chaotic behavior of the system. Also, the presented experimental results pave the way for using the proposed system in possible engineering applications such as data transmission and information security. [ABSTRACT FROM AUTHOR]

• The discrete-time mathematical model of the macroeconomic system is presented. • The system is studied through topological classification, bifurcation analysis, Lyapunov exponents, and manifold theory. • A fuzzy based-activation feedback controller is proposed for the synchronization of the system. Economic systems, due to their substantial effects on any society, are interesting research subject for a large family of researchers. Despite all attempts to study economic and financial systems, studies on discrete-time macroeconomic systems are rare. Hence, in the current study, we aim to investigate dynamical behavior and synchronization of these systems. At first, the discrete-time mathematical model of the macroeconomic system is presented. Then, the system is studied through topological classification, bifurcation analysis, Lyapunov exponents, and manifold theory, which are powerful tools in the investigation of nonlinear systems. This way, the features of the system are disclosed, and the existence of chaos in the system is shown. For the adequate performance of the economy, the economic systems are desired to operate in a unified manner. To this end, in the present research, a fuzzy based-activation feedback controller is proposed for the synchronization of the system. To enhance the celerity and accuracy of the proposed control for synchronization purposes, it is equipped with a fuzzy logic engine. Finally, the numerical simulations of the synchronization are presented and compared with those of a conventional activation feedback control. Numerical results verify that the proposed control technique can successfully push the states of the response system to the desired value. [ABSTRACT FROM AUTHOR]

• The effect of market confidence on a financial system from the perspective of fractional calculus. • Investigation of chaotic behavior of the system through numerical simulations and analyses, such as the Lyapunov exponents, bifurcation diagrams, and phase portraits. • Designing and implementing an analog circuit to prove the feasibility of the system in real-world applications. Modeling and analysis of financial systems have been interesting topics among researchers. The more precisely we know dynamic of systems, the better we can deal with them. This way, in this paper, we investigate the effect of market confidence on a financial system from the perspective of fractional calculus. Market confidence, which is a significant concern in economic systems, is considered, and its effects are comprehensively investigated. The system has been studied through numerical simulations and analyses, such as the Lyapunov exponents, bifurcation diagrams, and phase portrait. It is shown that the system enters chaos through experiencing a cascade of period doublings, and the existence of chaos is verified. Finally, an analog circuit of the chaotic system is designed and implemented to prove its feasibility in real-world applications. Also, through the circuit implementation, the effects of different factors on the behavior of the systems are investigated. [ABSTRACT FROM AUTHOR]

• Investigation of a mathematical model of the novel coronavirus • Pioneer research on policies regarding COVID-19 • A multi-objective genetic algorithm which proposes strategies to achieve high-quality schedules by adjusting various factors • The first research that proposes policies for COVID-19 by considering its economic consequences Understanding the early transmission dynamics of diseases and estimating the effectiveness of control policies play inevitable roles in the prevention of epidemic diseases. To this end, this paper is concerned with the design of optimal control strategies for the novel coronavirus disease (COVID-19). A mathematical model of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) transmission based on Wuhan's data is considered. To solve the problem effectively and efficiently, a multi-objective genetic algorithm is proposed to achieve high-quality schedules for various factors including contact rate and transition rate of symptomatic infected individuals to the quarantined infected class. By changing these factors, two optimal policies are successfully designed. This study has two main scientific contributions that are: (1) This is pioneer research that proposes policies regarding COVID-19, (2) This is also the first research that addresses COVID-19 and considers its economic consequences through a multi-objective evolutionary algorithm. Numerical simulations conspicuously demonstrate that by applying the proposed optimal policies, governments could find useful and practical ways for control of the disease. [ABSTRACT FROM AUTHOR]

• A novel optimization algorithm, called King, is introduced for solving variable-order fractional optimal control problems. • The structure of the proposed algorithm is precisely described. • The introduced method is verified using a chaotic financial system. • Also, the proposed algorithm is applied to several common optimization functions. In this study, a new optimization algorithm, called King, is introduced for solving variable order fractional optimal control problems (VO-FOCPs). The variable order fractional derivative is portrayed in the Caputo sense through the dynamics of the system as variable order fractional differential equation (VO-FDE). To this end, firstly, the VO-FOCP is converted into a system of VO-FDEs. Then, according to the fact that the VO-FDE is equivalent to a Volterra integral equation, the system of VO-FDEs is transformed into an equivalent system of variable order fractional integro-differential equations. In the next step, both the context of minimization of total error and a joint application of Banach's fixed-point theorem are used to solve a nonlinear optimization problem. Actually, using the existing mechanism, the synchronization problem is recast to an optimization problem. Due to the discretization and its board range of arbitrary nodes, the proposed method provides a very adjustable framework for direct trajectory optimization. Finally, the proposed algorithm is verified using several common optimization functions and a chaotic financial system. Also, through simulation results, the proposed method is compared with some popular methods. Simulation results demonstrate the appropriate performance of the introduced method. [ABSTRACT FROM AUTHOR]

• In this paper, we introduce a fractional-order hyperchaotic economic system. Additionally, the transient chaos phenomenon is detected for lower fractional orders. • The dynamical behavior of the system is numerically investigated using bifurcations diagrams, basins of attraction, and Lyapunov exponents. • We propose an adaptive terminal sliding mode control with neural network estimator for finite-time stabilization and synchronization of the fractional-order system. Moreover, the effects of external disturbances are fully taken into account with neural network estimator. We introduce for the first time a fractional-order hyperchaotic economic system. In this system, chaos generation depends upon the value of fractional-order. For certain fractional orders, a sustained regime of chaos is obtained. Also, the transient chaos phenomenon is detected for lower fractional orders. The dynamical behavior of the system is numerically investigated using bifurcations diagrams, basins of attraction, and Lyapunov exponents. Next, an adaptive terminal sliding mode control (ATSMC) with neural network estimator for finite-time stabilization and synchronization of the fractional-order system has been proposed. The radial basis function (RBF) neural network is used to achieve the estimation of the unknown function of the system. Also, the effects of external disturbances are fully taken into account with neural network estimator. The weights of the RBF neural network are updated based on the appropriate adaptation law. Using the fractional version of the Lyapunov stability theorem, the finite-time convergence of the closed-loop system has been proven. Finally, the new control technique is used for control and synchronization of the fractional-order hyperchaotic economic system. Simulation results illustrate the effectiveness of the proposed control scheme for uncertain fractional-order systems in the presence of external disturbances. [ABSTRACT FROM AUTHOR]

In the crucial arena of neurological care, pre-seizure, and seizure diagnosis stand as imperative focal points. While existing literature has probed this area, it demands sustained exploration given the intricate nature of seizures and the profound implications of prompt diagnosis on patient prognosis. Greater insights and novel advancements in the field of epilepsy diagnosis and prognosis can significantly bolster patient health and potentially redefine treatment management. Deep learning models like long short-term memory networks (LSTM) show promise for sequential data analysis. However, their application to electroencephalogram (EEG) signals for seizure detection reveals challenges, especially in imbalanced datasets. In response, we develop a hybrid graph neural network, integrating Convolutional Neural Networks (CNN) and LSTM through optimized skip connections. These connections, combined with our optimized graph structure, ensure no loss of crucial temporal data. The CNN layer efficiently extracts spatial features from samples, while LSTM emphasizes the EEG signal's temporal nuances. A unique facet of our proposed architecture is its optimized structure which is obtained based on Bayesian optimization. It does not merely refine network parameters but also systematically determines the optimal neuron count, layering, and overall architecture of our graph neural network. Alongside our deep learning methodology, we conduct a dynamical analysis elucidating the intrinsic chaotic patterns of seizure neural EEG signals. We demonstrate that the phase space analysis provides valuable insight for wavelet time-scale pre-processing for pre-seizure and seizure diagnosis. The numerical and empirical results validate the performance of our novel and breakthrough approach. Also, the results are compared with outcomes obtained using LSTM in different conditions. • Novel advancements in epilepsy diagnosis and prognosis can significantly bolster patient health and redefine treatment • A hybrid GNN with CNNs and LSTMs via optimized skip connections preserves key spatio-temporal brain neuroimaging data. • Our proposed architecture incorporates Bayesian optimization to calibrate, fine-tune and estimate the hyper-parameter space. • We uncover chaotic patterns in pre-seizure and seizure EEG signals, pre-processed via wavelet decomposition. • Empirical analysis shows our architecture exceeds established and current machine learning methods. [ABSTRACT FROM AUTHOR]

Having found hidden hyperchaos in a 5D self-exciting homopolar disc dynamo, we study the existence of a Hopf bifurcation, which leads to unstable limit cycles bifurcating from a stable equilibrium. Hidden chaos with only stable equilibria can be observed from the Hopf bifurcation: a typical way to enable hidden attractors to be located. We then provide a new fuzzy controller, and a fast fuzzy disturbance observer, based on terminal sliding mode control for synchronization of the hyperchaotic system. Fuzzy inference is considered to weaken the chattering phenomena. Using Lyapunov stability theory, the stability of the closed-loop system is proved. Finally, simulations of synchronization are illustrated to show the efficient performance of the designed control method via external disturbances and dynamic uncertainties. [ABSTRACT FROM AUTHOR]

This paper proposes a novel discrete locally active memcapacitor model and uses it to construct a novel memcapacitive hyperchaotic map. The fixed points and stability are analyzed, and the dynamical behaviors of the map with different parameters are studied in detail. In addition, special phenomena such as infinite coexisting attractors and intermittent chaos are discovered. Finally, the DSP implementation of the map is completed and the realizability of the theoretical analysis is demonstrated. The results of the theoretical analysis and digital circuit implementation show that the memcapacitive hyperchaotic map has rich dynamical behaviors and practical application potential. [ABSTRACT FROM AUTHOR]

This paper focuses primarily on the predefined-time stability for a class of fixed-time stable systems, with the least upper bound of the settling time as an explicit parameter. It is mathematically proved that the systems under consideration herein can reach stability within any preassigned time, rather than the overestimation of convergence time found in previous fixed-time stability. Comparisons show that our studied system is more general than some classical ones, and that many existing results can be derived. As an application of the exposed stability analysis, static and adaptive predefined-time control algorithms are designed to study the average consensus problem for nonlinear leaderless multi-agent systems. Particularly, the adaptive control protocol guarantees predefined-time consensus without requiring the global topology information of the systems under consideration. Numerical simulations are provided throughout to support our theoretical results. [ABSTRACT FROM AUTHOR]

We present a novel fault-tolerant prescribed performance control approach for fractional-order economic and supply chain systems. While faults and limitations are common in the economic realm, existing control methods for supply chains have not addressed these issues while they lack prescribed performance guarantees. To fill this gap, we propose a fault-tolerant control strategy that can ensure prescribed bounds for fractional three-echelon supply chains, even in the presence of faults and actuator failures. We provide a detailed design procedure and stability analysis, and validate our approach through simulations of supply chain control and synchronization. Our results demonstrate the efficacy of the proposed model. • Fault-tolerant control for fractional-order economic and supply chains ensures turbulence bounds in presence of faults • Robust control strategy maintains stability in three-echelon supply chains despite actuator failures • Supply chain control system proven robust through Lyapunov stability and proof by contradiction • Closed-loop stability achieved in the presence of unknown nonlinearities and faults • Simulations validate effectiveness of chaos suppression and synchronization [ABSTRACT FROM AUTHOR]

In today's sophisticated world, where financial systems play an increasingly important role, the application of controllers through management strategies is of crucial importance, given their vital role. An analysis of the synchronization of economic systems can provide a valuable insight into the financial synchronous development of different countries or regions around the world. In this paper, an adaptive fixed-time control strategy is presented for the function projective synchronization of drive-response hyperchaotic economic systems with unknown parameters and external perturbations. The developed controller is constructed by combining the fixed-time control approach and parametric adaptation technique. Specifically, the adaptive adjusting mechanisms are designed to estimate the unknown parameters and external perturbations, respectively. Stability investigation shows that the function projective synchronization errors under the developed controller can stabilize to the minor fields about zero in fixed time. A key feature of the developed controller is its high insensitive to unknown parameters and strong robustness against external perturbations. Finally, the effectiveness and merits of the presented control strategy are examined by simulation scenarios. • Introducing a novel adjustable fixed-time control strategy • Development of a robust controller by combining a fixed-time control approach with a parametric adaptation technique • Design of an adaptive adjusting mechanism to robust estimation of unknown time-varying parameters and external perturbations [ABSTRACT FROM AUTHOR]

Financial systems present nonlinear dynamics whilst in some conditions chaotic behaviours emerge, rendering the stability of these systems utterly volatile. In this novel study we investigate boom-bust cycles in stock markets with heterogeneous agent-based modeling, yet incorporating endogenously evolving fractions of market participants, particularly those switching between contrarian and fundamental strategies. The dynamical behavior of various market entry behaviours of market agents are studied via numerical simulations and analyses of phase portraits, bifurcation diagrams and Lyapunov exponents. If the system adjusts in a partial equilibrium of at least one positive Lyapunov exponent, we observe the emergence of chaotic dynamics. Overall, chaos emerges via endogenous boom-bust cycle dynamics, caused by time-varying fractions of switching strategies between contrarian versus fundamental trading strategies. Our results prove to be invaluable to different types of market participants, such as traders, arbitrageurs, investors, speculators and institutional market makers. • We investigate boom-bust cycles in financial markets with computational agent-based micro-modeling • Our novel approach incorporates evolving fractions of market entries switching between contrarian and fundamental strategies • Chaotic dynamics emerge endogenously due to time-varying fractions of heterogeneous market agents with adaptive expectations • Our scenario analysis uncovers chaotic dynamics that contribute to the observed boom-bust cycles in financial markets. • Our findings can be valuable for traders, arbitrageurs, investors, speculators and institutional market makers [ABSTRACT FROM AUTHOR]

In this article, a fixed-time neural control methodology is presented for the output-constrained synchronization of second-order chaotic systems with unknown parameters and perturbations. The presented controller is synthesized under the fixed-time backstepping control framework. In the virtual control law design, the barrier Lyapunov function (BLF) is introduced to tackle the output constraints. In the actual control law design, the neural network (NN) is embedded to identify the total unknown item. Stability argument shows that the resultant closed-loop system is practically fixed-time stable. A distinctive feature of the presented controller is that it is capable of stabilizing the synchronization errors in fixed time while ensuring the output constraints can always be satisfied simultaneously. The efficiency and superiority of the presented control methodology are examined through two simulated examples. • A fixed-time neural control methodology • Output-constrained synchronization of second-order chaotic systems • Fixed-time backstepping control framework [ABSTRACT FROM AUTHOR]

It is well known that the satellite attitude motion exhibits the chaotic phenomenon. This article addresses the challenging problem of chaotic attitude synchronization and anti-synchronization for master-slave satellites under unknown moments of inertia and disturbance torques. First, a fixed-time adaptive synchronization controller is designed by combining the fixed-time control technique and adaptive control technique. The parametric adaptation laws are adopted to identify the unknown parameters in the synchronization error system. Benefiting from the adaptive identifications, the proposed controller is highly robust to unknown moments of inertia and disturbance torques. The practical fixed-time stability of the resulting closed-loop system is strictly achieved. The proposed controller can guarantee all error variables in the closed-loop system regulate to the small residual sets around zero in fixed time. Then, a fixed-time adaptive anti-synchronization controller is developed in a similar way. Finally, simulations studies are conducted to demonstrate the effectiveness and excellent control performance of the proposed controllers. [ABSTRACT FROM AUTHOR]

• Identifying and predicting parameters of a symmetric chaotic fractional financial model using a novel algorithm. • Identifying time-varying fractional-order derivatives using a combination of differential evolution and Gaussian process. • Promoting and modifying of the extrapolation algorithm using a recurrent neural network. Identifying parameters of financial and economic models with chaotic dynamics is an important, yet daunting challenge because of the complexities there exist in these chaotic systems. Although several studies have been devoted to understanding the mechanism of financial systems, the application of most state-of-the-art methods to these systems is completely ignored. To the best of our knowledge, no study identifies and predicts fractional derivatives of economic models. The current study has been motivated by this issue. Employing the Differential Evolution algorithm, Gaussian process regression, and neural networks, we propose a novel algorithm to identify and predict parameters of a symmetric chaotic fractional financial model. In the first step, a combination of Differential Evolution and the Gaussian process is utilized to identify time-varying fractional-order derivatives. Then, through numerical simulation, it is demonstrated that although this method provides bright results for estimation and interpolation purposes, it fails to extrapolate and predict time-varying parameters. Hence, in the next step, by taking advantage of a recurrent neural network, the proposed method is promoted and modified for extrapolation. Numerical simulations firmly confirm the excellent performance of the improved algorithm for both interpolation and extrapolation purposes. [ABSTRACT FROM AUTHOR]