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End-to-end neural diarization (EEND) which has the capability to directly output speaker diarization results and handle overlapping speech has attracted more and more attention due to its promising performance. Although existing EEND-based methods often outperform clustering-based methods, they cannot generalize well to unseen test sets because fixed attractors are often utilized to estimate speech activities of each speaker. An iterative adaptive attractor estimation (IAAE) network was proposed to refine diarization results, in which the self-attentive EEND (SA-EEND) was implemented to initialize diarization results and frame-wise embeddings. There are two main parts in the proposed IAAE network: an attention-based pooling was designed to obtain a rough estimation of the attractors based on the diarization results of the previous iteration, and an adaptive attractor was then calculated by using transformer decoder blocks. A unified training framework was proposed to further improve the diarization performance, making the embeddings more discriminable based on the well separated attractors. We evaluated the proposed method on both the simulated mixtures and the real CALLHOME dataset using the diarization error rate (DER). Our proposed method provides relative reductions in DER by up to 44.8% on simulated 2-speaker mixtures and 23.6% on the CALLHOME dataset over the baseline SA-EEND at the 2nd iteration step. We also demonstrated that with an increasing number of refinement steps applied, the DER on the CALLHOME dataset could be further reduced to 7.36%, achieving the state-of-the-art diarization results when compared with other methods. [ABSTRACT FROM AUTHOR]

The way that the human brain handles the input variations has been one of the most interesting areas of research for neuroscientists. There are some evidences that the human brain acts like an attractor when trying to memorize or retrieve some information. Based on this fact, in this research, a new method is presented for creating attractors during training of an iterated autoencoder. In this method a new loss function is presented which decreases the absolute real of Eigen values while preserving the reconstruction error during training. A fully connected structure is chosen for constructing the iterated autoencoder in this research which mostly faces with local minima especially when they are deep. For getting through this issue, a layer-by-layer pre-training approach is taken to train the network. Using the evaluation on MNIST dataset, it is shown that the proposed model can retrieve 59.98% of test samples which shows a considerable improvement over Dense Associative Memory (DAM) when trained on 100 similar MNIST test samples. The performance of the proposed model is compared to overparameterized autoencoder (OAE) model which was recently presented and showed promising results in constructing associative memories. The results show that the proposed model outperforms OAE in terms of the number of attractors learned by the network in a similar number of network parameters. Finally, the performance of the proposed model is evaluated with corrupted version of training samples, revealing significant robustness when compared to the baseline autoencoder. [ABSTRACT FROM AUTHOR]

Generative Adversarial Networks (GANs) are well-known tools for data generation and semi-supervised classification. GANs, with less labeled data, outperform Deep Neural Networks (DNNs) and Convolutional Neural Networks (CNNs) in classification tasks. The success of GANs in classification tasks motivates the development of GAN-based techniques for semi-supervised regression tasks. However, developing GANs for regression introduces two major challenges: (1) inherent instability in the GAN formulation and (2) performing regression and achieving stability simultaneously. This paper introduces techniques that show improvement in the GANs' regression capability. We bake a differentiable fuzzy logic system at multiple locations in a GAN. The fuzzy logic takes the output of either the generator or the discriminator to predict the output, y , and evaluate the generator's performance. We outline the results of applying the fuzzy logic system across multiple GANs and summarize each approach's efficacy. This paper shows that adding a fuzzy logic layer can enhance GAN's ability to perform regression; the most desirable injection location is problem-specific, and we show this through experiments over various datasets. Besides, we demonstrate empirically that the fuzzy-infused GANs are competitive with the DNNs. [ABSTRACT FROM AUTHOR]

• We proposed a deep-learning-based model for perceptual speech quality assessment. • We presented an application of this model as perceptual regularization for speech enhancement. • Experimental results show significant improvement in the enhanced speech naturalness. Many speech enhancement methods require perceptual quality metrics for evaluation. The "holy grail" of perceptual speech quality assessment is human subjective ratings, known as the mean opinion score. However, acquiring human ratings is time-consuming, laborious, and expensive. Existing objective quality metrics, on the other hand, are efficient and easy to compute but do not correlate well with human ratings. In this paper, we propose a relatively lightweight deep-learning-based model to predict the human ratings of speech signals. Since it is differentiable, it can be easily employed as a perceptual regularization to improve existing deep-learning-based speech enhancement methods. Experimental results demonstrate that the predictions of our proposed model correlate well with human judgments. We present application in speech enhancement and show that, interestingly, while there is a degradation in performance in terms of traditional objective metrics, there is a significant improvement in the perceptual quality and the naturalness of the enhanced speech. [ABSTRACT FROM AUTHOR]

Kernel methods have been successfully used to learn surrogate models for dynamical systems by regressing the vector field of such systems. However, choosing an appropriate kernel for a specific problem is an essential challenge in practice. Kernel Flows (KFs) have emerged as an effective tool for learning data-adaptive kernels used to interpolate dynamical systems. In this paper, we introduce Hausdorff Metric based Kernel Flows (HMKFs) to discover a'good' kernel from time series when a system under consideration has an attractor. First, under the premise that a kernel is good if there is no significant loss in accuracy when half of the data is used to reconstruct the attractor, we design an objective function based on the distance between true and forecasted attractors. Then, we optimize the proposal by adding an ℓ 1 penalty term when the base kernel contains many terms, thereby generating sparse HMKFs. Furthermore, we apply HMKFs and its sparse version to a library of 133 chaotic systems from various fields such as biochemistry, fluid mechanics, and astrophysics. The results showcase the potential of HMKFs in accurately modeling complex dynamical systems using data-driven kernels. • Comprehensive Review: The paper provides an extensive overview of machine learning methods for time series analysis. • Kernel-Based Methods: Highlights the advantages of kernel-based methods for their robustness and interpretability. • Hausdorff Metric Based Kernel Flows (HMKFs): Introduces HMKFs for optimal kernel identification in systems with attractors, using reduced data. • Sparse Kernel Flows: Enhances HMKFs efficiency by sparsifying the base kernel using ℓ 1 -regularization. • Applications and Experiments: Applies HMKFs to 133 chaotic systems, demonstrating efficacy, with detailed numerical experiments validating performance. [ABSTRACT FROM AUTHOR]

In this paper, we propose a dual-mixed formulation for stationary viscoplastic flows with yield, such as the Bingham or the Herschel-Bulkley flow. The approach is based on a Huber regularization of the viscosity term and a two-fold saddle point nonlinear operator equation for the resulting weak formulation. We provide the uniqueness of solutions for the continuous formulation and propose a discrete scheme based on Arnold-Falk-Winther finite elements. The discretization scheme yields a system of slantly differentiable nonlinear equations, for which a semismooth Newton algorithm is proposed and implemented. Local superlinear convergence of the method is also proved. Finally, we perform several numerical experiments in two and three dimensions to investigate the behavior and efficiency of the method. [ABSTRACT FROM AUTHOR]

In this work, we discuss the controllability and observability behaviors of a non-homogeneous conformable fractional dynamical system (C-FDS) based on the conformable fractional exponential matrix (C-FEM) and fractional Grammian matrix (FGM). Moreover, the nice relationships between controllability, observability , and stability for non-homogeneous C-FDS are derived. To demonstrate the effectiveness of our obtained results, we present the general solutions (GSs), controllability, observabilities and stabilities to three attractive physical and engineering problems related to compatibility with conformable fractional electrical circuits (C-FECs). Finally, the fractional and classical behaviors of each problem have been covered, respectively, when α = 1 2 and α = 1. [ABSTRACT FROM AUTHOR]

Due to the non-smoothness of the Hinge loss in SVM, it is difficult to obtain a faster convergence rate with modern optimization algorithms. In this paper, we introduce two smooth Hinge losses ψ G (α ; σ) and ψ M (α ; σ) which are infinitely differentiable and converge to the Hinge loss uniformly in α as σ tends to 0. By replacing the Hinge loss with these two smooth Hinge losses, we obtain two smooth support vector machines (SSVMs), respectively. Solving the SSVMs with the Trust Region Newton method (TRON) leads to two quadratically convergent algorithms. Experiments in text classification tasks show that the proposed SSVMs are effective in real-world applications. We also introduce a general smooth convex loss function to unify several commonly-used convex loss functions in machine learning. The general framework provides smooth approximation functions to non-smooth convex loss functions, which can be used to obtain smooth models that can be solved with faster convergent optimization algorithms. [ABSTRACT FROM AUTHOR]

The Earth system is often modeled as a dynamical system in what has come to be known as Earth System Models. When used to study anthropogenically forced climate change, these models are forced in such a way that they are not in a statistically stationary state. Yet, statistical statements are still made about the Earth climate system using only a single trajectory by taking temporal averages. At each moment in time, one draws a sample from a different distribution, raising questions about the utility of temporal averages, in stark contrast to the utility of temporal averages in ergodic systems. This work follows in the tradition of using a toy model to examine properties present in the Earth climate system. We aim to examine how we can make meaningful statistical statements in non-stationary systems when only dealing with a single trajectory. We use the Lorenz equations with a time-varying parameter as a starting point for comparing ensemble averages to temporal averages. We find that, in so far as the control parameter induces a slow and smooth change in the dynamics, the resulting statistics of ensemble averages compare well to those of temporal averages. • A Markov chain-based methodology for the study of non-stationary dynamical systems. • Evolution of statistics in Lorenz system with a time-varying parameter is studied. • Given slowly-varying parameters, temporal averages correspond to ensemble averages. • Extension of methodology to study statistics in a changing climate is discussed. [ABSTRACT FROM AUTHOR]

This paper studies the structural stability of periodic solutions for first-order fuzzy differential equations (FDEs) understood as differential inclusions, i.e., first-order uncertain dynamical systems. The existence and uniqueness of periodic solutions for this first-order fuzzy problems have been obtained on general fuzzy number space. When the forcing function has specific perturbations, the structural stability of the periodic solutions are discussed by using the support function, the Dini Theorem and the Convergence Theorem in the differential inclusion theory. [ABSTRACT FROM AUTHOR]

This paper investigates the leader-following bipartite consensus problem for second-order multi-agent systems with nonlinear dynamics, node-delay and signed digraph topology. By using pinning control strategies, an event-triggered controller is designed to achieve bipartite consensus in multi-agent systems, where a novel event-triggered function is proposed. Two cases are discussed in this paper according to whether the node-delay is differentiable or not. When the node-delay is differentiable, an LMI (Linear Matrix Inequality) condition is derived for reaching bipartite consensus in multi-agent systems by using M -matrix theory. When the node-delay is non-differentiable, some bipartite consensus conditions are developed based on Jensen inequality and the reciprocally convex approach. Moreover, it is shown that Zeno-behavior can be avoided for the designed event-triggered controller. Finally, some numerical examples are provided to illustrate the effectiveness and correctness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

Moisture/air-flow over the aircraft wing and bonnet of a moving car in aerodynamical systems exhibit dynamic behavior characterized by accelerating and decelerating flows. These analysis is essential and applicable in various fields, including physics, engineering, and fluid mechanics. The present investigation aim to explore the dynamics of accelerating and decelerating flows within the framework of boundary layer examination. To achieve these objectives, a non-similar group of transformations is employed to convert the governing dimensional two-variable dynamical system into a dimensionless differential form, with η and ξ as the independent variables. To gain physical understanding of the mathematical equations governing the flow, an efficient bivariate spectral collocation method (BSCM) is employed for analyzing the flow dynamics. This method allows for a thorough investigation of the behavior and characteristics of the accelerating and decelerating Casson flows. Subject to the convergence and residual error analysis of the numerical results, the effects of pertinent parameters on the flow variables were investigated. The findings of this study show that the effects of flow parameters on decelerating and accelerating flows are not completely opposite. Additionally, the Biot parameter positively impacts the velocity and temperature profiles of the two dynamical flows. However, an increase in the Casson fluid parameter β has an opposing effect on the temperature and concentration profiles of both flows. • Boundary layer over an inclined plate. • Non-similar solution for natural convection flow. • Effect of thermal radiation on boundary layer flow. • Casson fluid flow over an inclined plate. [ABSTRACT FROM AUTHOR]

Using renewal times and Girsanov's transform, we prove that the speed of the excited random walk is infinitely differentiable with respect to the bias parameter in (0 , 1) in dimension d ≥ 2. At the critical point 0, using a special method, we also prove that the speed is differentiable and the derivative is positive for every dimension 2 ≤ d ≠ 3. However, this is not enough to imply that the speed is increasing in a neighborhood of 0. It still remains to prove that the derivative is continuous at 0. Moreover, this paper gives some results of monotonicity for m -excited random walk when m is large enough. [ABSTRACT FROM AUTHOR]

A range of new fractional-order love dynamics is modelled in this paper using the Caputo (power-law), Caputo–Fabrizio (exponential decay-law) and Atangana–Baleanu (Mittag-Leffler-law) fractional operators. We utilize the new fractional Adams–Bashforth schemes for the approximation of these derivatives. This method was developed with the standard differentiation technique by applying the fundamental theorem of calculus and taking the difference of two times levels at t = (t n , t n + 1). The stability analysis applies the theory of classical order differential equations and dynamical system. The Existence and uniqueness of solution of fractional dynamics is proved by adopting the fixed-point theorem. Numerical results presented for various α − values justify the theoretical findings. It was observed that modelling of interpersonal and romantic love affairs with fractional derivative could exhibit some strange emotional attractors. • Fractional two-step Adams–Bashforth methods. • Numerical approximation and simulation. • Existence and uniqueness of solutions via fixed-point theorem. • The Caputo, Caputo–Fabrizio and Atangana–Baleanu fractional derivatives. [ABSTRACT FROM AUTHOR]

Abstract We study first-order nonlinear planar Hamiltonian boundary value problems on time scales. Estimates on lower bounds for the eigenvalues of the problems are established by way of the Lyapunov inequality method. Our results are interpreted to nonlinear differential and difference planar Hamiltonian boundary value problems. As a special case, an estimate on lower bounds for eigenvalues of half-linear dynamic equations is obtained which generalizes and improves the existing ones to nonlinear Hamiltonian systems. Based on the main results, we establish existence and uniqueness of solutions of a related linear boundary value problem. [ABSTRACT FROM AUTHOR]

Abstract Multimodal optimization, aiming to locate multiple optima in parallel, is a challenging task. In this paper, a multilevel sampling strategy based memetic differential evolution algorithm is proposed to tackle the problem. In the proposed algorithm, a multilevel sampling strategy is devised to sample a subpopulation for evolution at each generation. In this strategy, the entire population is dynamically divided into multiple levels according to the fitness of individuals at each generation. A subpopulation is then adaptively sampled from the individuals at different levels to undergo a niching based evolution for identifying multiple optima in the search space. Further, a crossover-based local search scheme is designed to fine-tune the seed solutions of niches in the population during evolution. We evaluate the proposed method on 20 benchmark multimodal problems and compare it with state-of-the-art multimodal optimization algorithms. The results show that our proposed algorithm can effectively and accurately locate multiple optima, outperforming related methods to be compared. [ABSTRACT FROM AUTHOR]

Abstract The paper concerns the existence of rotating periodic solutions in Hamiltonian systems. This kind of rotating periodic solutions has the form of x (t + T) = Q x (t) with some symplectic orthogonal matrix Q. When Q k = I for some integer k > 0 , it is a symmetric periodic solution and when Q k ≠ I for any k ∈ N + , it is just a quasi-periodic one corresponding to a rotation. It is proved that if the Hamiltonian is strictly convex, coercive and Q invariant, then there exists a Q -rotating periodic solution on every energy surface. [ABSTRACT FROM AUTHOR]

In this paper, we describe string attractors of all factors of episturmian sequences and show that their size is equal to the number of distinct letters contained in the factor. [ABSTRACT FROM AUTHOR]

This article deals with the problem of the existence of solution for a class of first-order fuzzy differential equations in dual form in the sense that the derivative of the unknown function appears on both sides of the equation. The problem is studied from the point of view of the generalized Hukuhara differentiability and sufficient conditions for the existence of a unique solution are provided, in details. Also, iterative sequences converging to the solutions are presented and applied to solve some numerical examples. Finally, a practical application of the results is brought. [ABSTRACT FROM AUTHOR]

Quasiperiodically forced systems are an important class of dynamical systems exhibiting quasiperiodic, strange nonchaotic, and chaotic attractors. A major concern is the identification of the parameter range in which each one of the attractors is present. In this work, based on the phase sensitivity proposed by Pikovsky and Feudel, we define a measure to quantitatively distinguish quasiperiodic attractors, strange nonchaotic attractors, and chaotic attractors. Particularly, we can determine the boundary points of these three attractors in parameter space. The reliability of this measure is verified in smooth and non-smooth systems. • The strange property of attractors in quasiperiodically forced systems is studied. • A measure is defined to quantitatively distinguish the types of attractors. • The reliability of the measure is verified in smooth and non-smooth systems. [ABSTRACT FROM AUTHOR]

For a static economic model of auto traffic in an isotropic zone, this paper classifies possible equilibria into three types, by whether traffic is hypercongested and by the relative slopes of "supply" and "demand" curves. We then conduct a local stability analysis of each type when density, demand and the unit travel time (inverse speed) evolve gradually and simultaneously according to dynamical systems of differential equations. Some hypercongested equilibria may be stable when demand adjusts quickly enough to congestion. Other hypercongested equilibria, which have counterintuitive comparative statics, are never stable. Non-hypercongested equilibria can be unstable under special circumstances. A discrete event simulation with a dynamic Poisson arrival process supports the results of the formal analysis. • Examines equilibrium stability for a static model of traffic in an isotropic zone with elastic demand. • Builds autonomous systems governing how density, demand and speed adjust. • Some hypercongested equilibria can be stable if demand adjusts quickly enough. • Non-hypercongested equilibria can be unstable under special circumstances. • Validates results using a trip-based simulation with a dynamic Poisson arrival process. [ABSTRACT FROM AUTHOR]

Abstract The generalized variational principle of Herglotz type provides a variational method for describing nonconservative or dissipative processes. The purpose of this letter is to extend this variational principle to a first order linear nonholonomic system and study the conservation laws of the nonconservative nonholonomic system based on Herglotz variational problem. A new differential variational principle of the nonconservative nonholonomic system is proposed, which is based on Herglotz variational problem. And the differential equations of motion of the system are also obtained. Then, according to the condition for the invariance of the differential variational principle, the conservation theorem based on Herglotz variational problem for the nonconservative nonholonomic system are obtained. The theorem contains the conservation theorem of the nonconservative holonomic system as its special case, which can be reduced to the first Noether's theorem based on Herglotz variational problem under proper conditions. The inverse theorem of the conservation theorem is also provided and proved. An example is given to illustrate the application at the end of this letter. Highlights • Herglotz variational principle of a nonholonomic system is proposed firstly. • The conditions of invariance for a nonholonomic system of Herglotz type are given. • Conservation laws of holonomic and nonholonomic nonconservative systems are obtained. • The corresponding inverse theorem of the conservation theorem is established. • A special case is discussed to illustrate the application of the results we obtained. [ABSTRACT FROM AUTHOR]

Abstract A graph G is Hamilton-connected if for any pair of vertices v and w, G has a spanning (v, w)-path. Extending theorems of Dirac and Ore, Erdős prove a sufficient condition in terms of minimum degree and the size of G to assure G to be Hamiltonian. We investigate the spectral analogous of Erdős’ theorem for a Hamilton-connected graph with given minimum degree, and prove that there exist two graphs { L n k , M n k } such that each of the following holds for an integer k ≥ 3 and a simple graph G on n vertices. (i) If n ≥ 6 k, δ (G) ≥ k , and | E (G) | > (n − k 2) + k (k + 1) , then G is Hamilton-connected if and only if C n + 1 (G) ∉ { L n k , M n k }. (ii) If n ≥ max { 6 k , 1 2 k 3 − 1 2 k 2 + k + 4 } , δ (G) ≥ k and spectral radius λ (G) ≥ n − k , then G is Hamilton–connected if and only if G ∉ { L n k , M n k }. [ABSTRACT FROM AUTHOR]

Abstract In this note we generalize the Ball-James rigidity theorem for gradient differential inclusions to the setting of a general linear differential constraint. In particular, we prove the rigidity for approximate solutions to the two-state inclusion with incompatible states for merely L 1 -bounded sequences. In this way, our theorem can be seen as a result of compensated compactness in the linear-growth setting. [ABSTRACT FROM AUTHOR]

An inverse problem for differential pencils of second order is studied. We show that the potentials on the whole interval can be uniquely determined by partial information on potentials and parts of two spectra. [ABSTRACT FROM AUTHOR]

Abstract In this paper we introduce a concept of weak stability for non-autonomous dynamical systems. We characterize the set of weak stable points and show that the set of weak stable points is residual, and investigate the relation between weak stability and shadowing property. We also discuss the relation between weak stability of a non-autonomous dynamical system and its induced set-valued system. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a novel three-dimensional fractional-order chaotic system without linear terms is proposed. Compared with other similar fractional-order chaotic systems, this system has two striking and unique features: (i) it exhibits robust chaotic behavior (i.e., sustained chaotic behavior) with respect to parameter b and more interestingly, the corresponding largest Lyapunov exponent becomes increasingly big with the increase of the parameter b ; (ii) it can generate two twin symmetric strange attractors when the simulation time is reversed. To our knowledge, such a three-dimensional fractional-order chaotic system holding these two special features simultaneously has never been reported. Using standard nonlinear dynamical analysis tools including phase portraits, equilibrium stability, Poincaré map, bifurcation diagram, Lyapunov exponents and spectral entropy complexity, the complex dynamical behaviors of the system are systematically analyzed and investigated. And the complexity results well matches with that of the bifurcation diagrams, showing complexity can well reflect the dynamical properties of this fractional-order chaotic system. Furthermore, to validate the correctness and practical feasibility of the system under study, hardware electronic circuits with different fractional orders are designed. And the corresponding experimental results are also presented to confirm the theoretical analysis. Highlights • A novel three-dimensional fractional-order chaotic system without linear terms is proposed. • The system exhibits robust chaotic behavior with respect to one of system parameters. • The system generates two twin symmetric strange attractors when time is reversed. • Hardware circuits with different fractional orders are designed to confirm the theoretical analysis. [ABSTRACT FROM AUTHOR]

Social network is an important carrier of information diffusion, and social tie is one of most significant factors between them. To understand the impact of social tie on information dissemination, a dynamical model with social tie strength and self-confirming mechanism is proposed and analyzed in this paper. Theoretical analysis indicates that the equilibrium of the proposed model is globally asymptotically stable, and social tie plays a key role in information propagation. Finally, some numerical simulations under synthetic networks and a partial Facebook network are given to illustrate the main results. [ABSTRACT FROM AUTHOR]

Chaotic return maps are widely used to model various dynamical systems such as charged particle movement, laser beam dynamic, celestial body orbiting and many others. Return maps are commonly obtained by discretization of continuous equations using the Euler–Cromer operator with the only motivation that it is the simplest symplectic operator. Recent progress in geometric integration raised considerable interest to symmetric operators due to their ability to preserve some geometric properties of continuous flows this way yielding better agreement between discrete and continuous dynamical systems. Here we compare symmetric and asymmetric discretization approaches applied to several examples of Hamiltonian systems. In particular, we suggest symmetric modifications of Chirikov and Hénon maps and show explicitly that the implied symmetric integration procedure yields reflectional symmetry in the phase space. For verification, we show that a smooth even perturbation function used instead of a discontinuous delta pulse provides asymptotically similar results. Numerical experiments using several statistical methods show that symmetric and asymmetric maps, while yielding similar asymptotic behavior, often exhibit considerably different statistical properties for intermediate regimes providing smoother transitions that are more reminiscent to those observed in various natural phenomena. We believe that the proposed approach may be useful for modeling empirical systems by preserving their keynote physical properties. [ABSTRACT FROM AUTHOR]

Graphical abstract Key findings (1) DC-WCA is faster in finding better solutions for benchmark problems, compared to the other reported optimizers. (2) The performance of DC-WCA is highly competitive with the other reported optimizers for the multi-reservoir optimization. Fig. 1 Comparison of ICGA, CPSO, WCA, and DC-WCA: (a) Benchmark problems; (b) Case study for multi-reservoir optimization. Highlights • A modified water cycle algorithm based on diversity evaluation and chaos theory (DC-WCA) is proposed. • The performance of DC-WCA is validated by six benchmark problems. • DC-WCA is applied for a long-term multi-reservoir optimization. • DC-WCA is faster in finding better hydropower generation for multi-reservoir system, compared to other reported optimizers. Abstract Hydropower generation is a common consideration for reservoir operations. Due to the characteristic of high dimensionality, multi-reservoir optimization for hydropower generation is challenging. Although the original water cycle algorithm (WCA) outperforms other metaheuristic optimization algorithms in solving constrained and unconstrained problems, it still gets trapped in the local optima in the case of some high-dimensional problems. For multi-reservoir optimization problems, this paper provides a modified WCA based on the diversity evaluation and chaos theory (DC-WCA) to avoid premature convergence. Six benchmark problems are examined using DC-WCA, WCA, improved chaos genetic algorithm (ICGA) and chaotic particle swarm optimization algorithm (CPSO) to evaluate the efficacy of DC-WCA. To investigate the application of DC-WCA for multi-reservoir optimization, a serially linked reservoir system located in the upper reach of the Yangtze river of China is used as a case study. After sensitivity analyses of the parameters, the four algorithms are used for long-term multi-reservoir optimization for hydropower generation. The optimization results show that 1) the annual hydropower generation optimized using DC-WCA is superior to those optimized using the other reported optimizers, and 2) the convergence rate of DC-WCA is faster than those of the other reported optimizers. This case study indicates that the application of DC-WCA for multi-reservoir optimization not only improves the calculation accuracy but also reduces computation time. [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Introducing a new algorithm named chaotic-based crow search algorithm (CCSA). • Four variants of the CCSA are introduced and the best one is chosen. • The proposed CCSA algorithm is validated on fifteen FOPs. • The solution of the fractional formulation of the fractional economic, environmental power dispatch problem is investigated. • Results prove that the superiority of CCSA regarding the obtained powerful results. Abstract This paper presents a chaotic crow search algorithm (CCSA) for solving fractional optimization problems (FOPs). To refine the global convergence speed and enhance the exploration/exploitation tendencies, the proposed CCSA integrates chaos theory (CT) into the CSA. CT is introduced to tune the parameters of the standard CSA, yielding four variants, with the best chaotic variant being investigated. The performance of the proposed CCSA is validated on twenty well-known fractional benchmark problems. Moreover, it is validated on a fractional economic environmental power dispatch problem by attempting to minimize the ratio of total emissions to total fuel cost. Finally, the proposed CCSA is compared with the standard CSA, particle swarm optimization (PSO), firefly algorithm (FFA), dragonfly algorithm (DA) and grey wolf algorithm (GWA). Additionally, the efficiency of the proposed CCSA is justified using the non parametric Wilcoxon signed-rank test. The experimental results prove that the proposed CCSA outperforms other algorithms in terms of quality and reliability. [ABSTRACT FROM AUTHOR]

We investigate the dynamical behavior of the newly introduced dual power Zakharov–Kuznetsov–Burgers equation. Using bifurcation theory of planar dynamical systems, we study bifurcations of traveling wave solutions of the dual power Zakharov–Kuznetsov–Burgers equation in presence and absence of viscosity ( μ ) effect. In presence of an external periodic perturbation, we discuss the periodic and chaotic motions of the perturbed dual power Zakharov–Kuznetsov–Burgers equation by analyzing phase projection analysis, time series analysis, Poincaré section and sensitivity analysis. The effect of viscosity ( μ ) plays an important role in the transition from chaotic motion to periodic motion of the perturbed dual power Zakharov–Kuznetsov–Burgers equation. [ABSTRACT FROM AUTHOR]

We consider Hamiltonian systems driven by multi-dimensional Gaussian processes in rough path sense, which include fractional Brownian motions with Hurst parameter H ∈ ( 1 / 4 , 1 / 2 ] . We prove that the phase flow preserves the symplectic structure almost surely and this property could be inherited by symplectic Runge–Kutta methods, which are implicit methods in general. If the vector fields satisfy some smoothness and boundedness conditions, we obtain the pathwise convergence rates of Runge–Kutta methods. When vector fields are linear, we get the solvability of the midpoint scheme for skew symmetric cases, and obtain its pathwise convergence rate. Numerical experiments verify our theoretical analysis. [ABSTRACT FROM AUTHOR]

In recent years, various chaotic systems have been introduced in literature to be used in different branches of science. In the field of secure chaotic communication, more complex chaotic systems are proposed, such as high dimensional (4D, 5D), multi-scroll, surface equilibrium point, to enhance communication security level. In this study, a chaotic system owning logic element is used for increasing the level of security of chaotic communication system, which has not been previously implemented for this purpose in the literature. The used chaotic system includes signum functions, maximum function and absolute operation term. Also, there are analog devices and digital device in the electronic circuit of this chaotic system. These properties increase the complexity of the chaotic system and the security level. Sliding mode control method is preferred for the synchronization part of the secure communication. In this regard, numerical analysis and electronic circuit design of the secure chaotic communication system by using the chaotic system owning logic element have been performed successfully. [ABSTRACT FROM AUTHOR]

In this paper, a Galerkin energy-preserving scheme is proposed for solving nonlinear Schrödinger equation in two dimensions. The nonlinear Schrödinger equation is first rewritten as an infinite-dimensional Hamiltonian system. Following the method of lines, the spatial derivatives of the nonlinear Schrödinger equation are approximated with the aid of the Galerkin methods. The resulting ordinary differential equations can be cast into a canonical Hamiltonian system. A fully-discretized scheme is then devised by considering an average vector field method in time. Moreover, based on the fast Fourier transform and the matrix diagonalization method, a fast solver is developed to solving the resulting algebraic equations. Finally, the proposed scheme is employed to capture the blow-up phenomena of the nonlinear Schrödinger equation. [ABSTRACT FROM AUTHOR]

A unique method for forecasting Hopf bifurcations and the complete post-bifurcation dynamics of nonlinear oscillatory systems is proposed. The method is model-less and uses measurements of the system only in the pre-bifurcation regime. The forecasts are three-dimensional bifurcation diagrams using a few measurements of the system response to perturbations in the pre-bifurcation regime. To demonstrate the forecasting method and its advantages, it is employed to predict bifurcation diagrams of a 3-DOF fluid-structural system. Surrogate measurement data is obtained from simulations and used as input for the forecasting algorithm. Results show that the bifurcation diagrams are forecasted accurately in both supercritical and subcritical bifurcations. The method accurately forecasts the bifurcation point, the bifurcation type and the post-bifurcation limit cycle amplitudes despite the fact that only pre-bifurcation regime data are used for forecasting. [ABSTRACT FROM AUTHOR]

Varying the free-stream turbulence intensity (T i = 0%, 5%, 10%) the flow over a circular cylinder for Re = 3900 is examined using high fidelity eddy-resolving simulations. Results show that with growth of the turbulence intensity, the drag coefficient increases and the pressure base coefficient drops, as well as the flow bifurcation in the near wake occurs, when the length of the separation zone is reduced by about two, and the stream velocity profile is reshaped from U-shaped to V-shaped. The flow transformation is accompanied by the separation of the wall stress scales. At the same time, dynamics of the vortex shedding (Strouhal number) remains unchanged. The flow bifurcation, confirmed experimentally in practice, and the phase transition are examined using the Lyapunov metric (predictability time and phase-space diagrams). The predictability times, i.e. the phase transition between the two states T i = 0% → 5% and T i = 0% → 10% are estimated at one half and one of the characteristic convective time, after which the saturation occurs when both dynamical systems reach a statistical stationary state. Finally, phase-space states are visualized in 2D and 3D, and shown that related attractors can be bounded by simple geometrical ellipsoids. • LES of the flow over a circular cylinder at Re=3900 is presented. • Impact of the free stream turbulence intensity (0%, 5% and 10%) is investigated. • Bifurcation is identified by increasing of the free-stream turbulence intensity. • Visualization of phase-states and attractors is provided. [ABSTRACT FROM AUTHOR]

Multistability is an important concept that refers to the coexistence of multiple solutions. Although significant studies reported the emergence of multistability, a few studies have been devoted to investigating its features. This paper is dedicated to addressing the volume dependence of multistability as its extensive feature using theoretical and numerical aspects. The results of the forward and backward dynamical analysis of the modulated laser system and the Duffing oscillator show that multistability takes place when the attractor volume becomes large enough to meet other solutions. On the other hand, when the attractor volume is small, the system solution has no chance to visit other attractors, and multistability cannot occur. Furthermore, our results suggest that the dissipation diagram, which is normalized to the attractor volume, can detect the multistability regions since it simultaneously includes information about the dissipation and attractor volumes. • The volume dependence of multistability is addressed as its extensive feature. • Theoretical and numerical aspects are provided to support the idea. • Multistability occurs when the attractor volume grows large enough to encounter other solutions. • Small attractor volumes prevent the emergence of multistability since the system solution cannot visit other attractors. • The multistability regions can be detected using the dissipation diagram normalized to the attractor volume. [ABSTRACT FROM AUTHOR]

A 4D hyperchaotic system with symmetry based on memristors is proposed and the chaotic properties of the circuit are verified by phase diagrams, Poincaré cross sections, bifurcation, Lyapunov exponents, and 0–1 tests. In addition, the system is found to have rich dynamical behaviors such as transient chaos, intermittent chaos, offset enhancement, burst oscillation, and infinite attractor coexistence. The complexity comparison analysis reveals that this hyperchaotic system has good symmetry as well as the initial values of the system that are more suitable for image encryption. Circuit simulation of the system using simulation software proved the usability of the system. A field programmable gate array (FPGA) is used to implement the actual digital circuit of the system. The final FPGA results agree with the numerical simulation and prove the practical value of the constructed memristor hyperchaotic system. Finally, chaotic circuits are applied to DNA image encryption. It is discovered to have a very large key space, strong key sensitivity, outstanding anti-cropping, noise immunity and high security performance. Thus, the proposed hyperchaotic system has good advantages for application in the field of image encryption. [Display omitted] • Because of its special physical properties, memristor can help chaotic circuits to get richer dynamic behavior. • The attractor coexistence of chaotic circuits can be used more widely in the field of image encryption. • Explosive oscillation is a rare characteristic of chaotic systems. • The combination of chaotic system and encryption algorithm can improve the security of data transmission. [ABSTRACT FROM AUTHOR]

In the commented paper, the authors consider a three-dimensional system and analyze the presence of Shilnikov chaos as well as a Hopf bifurcation. On the one hand, they state that the existence of a chaotic attractor is verified via the homoclinic Shilnikov theorem. The homoclinic orbit of this system is determined by using the undetermined coefficient method, introduced by Zhou et al. in [Chen's attractor exists, Int. J. Bifurcation Chaos 14 (2004) 3167–3178], a paper that presents very serious shortcomings. However, it has been cited dozens of times and its erroneous method has been copied in lots of papers, including the commented paper where an even expression for the first component of the homoclinic connection is used. It is evident that this even expression cannot represent the first component of a Shilnikov homoclinic connection, an orbit which is necessarily non-symmetric. Consequently, the results stated in Section 3, the core of the paper, are worthless. On the other hand, the study of the Hopf bifurcation presented in Section 4 is also wrong because the first Lyapunov coefficient provided by the authors is incorrect. [ABSTRACT FROM AUTHOR]

With the rapid economic growth in recent years, the peak operation of hydropower system (POHS) is becoming one of the most important optimization problems in power system. However, the rapid expansion of system scale, refined management and operational constraints has greatly increased the optimization difficult of POHS. As a result, it is of great importance to develop effective methods that can ensure the computational efficiency of POHS. The progressive optimality algorithm (POA) is a commonly used technique for solving hydropower operation problem, but its execution time still grows sharply with the increasing number of hydropower plants, making it difficult to satisfy the efficiency requirement of POHS. To address this problem, a novel efficient method called parallel progressive optimality algorithm (PPOA) is presented in this paper. In PPOA, the complex problem is firstly divided into several two-stage optimization subproblems, and then the classical Fork/Join framework is used to realize parallel computation of subproblems, making a significant improvement on execution efficiency. The simulations in a real-world hydropower system demonstrate that as compared with the standard POA, PPOA can use abundant multi-core resources to reduce execution time while keeping the quality of solution, providing a new alternative to solve the complex hydropower peak operation problem. [ABSTRACT FROM AUTHOR]