Results 1 - 10 of 1953
Results 1 - 10 of 1953. Search took: 0.024 seconds
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[en] Highlights: • Hindmarsh–Rose neuron model is analyzed analytically and numerically • Atangana–Baleanu fractional derivative in Caputo sense is used in the modeling • The system reveals existence of equilibria whose some are unstable • It also reveals a system with initially regular bursts that evolve into chaos • Repeated bursts happen to occur more rapidly in time as derivative order decreases - Abstract: Recent discussions on the non validity of index law in fractional calculus have shown the amazing filtering feature of Mittag–Leffler function foreseing Atangana–Baleanu derivative as one of reliable mathematical tools for describing some complex world problems, like problems of neuronal activities. In this paper, neuronal dynamics described by a three dimensional model of Hindmarsh–Rose nerve cells with external current are analyzed analytically and numerically. We make use of the Atangana–Baleanu fractional derivative in Caputo sense (ABC derivative) and asses its impact on the dynamic, especially the role played by its derivative order in combination with another control parameter, the intensity of the applied external current. Our analysis proves existence of equilibria whose some are unstable of type saddle point, paving the ways for possible bifurcations in the process. Numerical approximations of solutions reveal a system with initially regular bursts that evolve into period-adding chaotic bifurcations as the control parameters change, with precisely the Atangana–Baleanu fractional derivative’s order decreasing from 1 down to 0.5.
[en] Highlights: ●Singular systems theory together with fractional calculus is utilized to model the logistic growth, and a fractional-order singular (FOS) logistic map is introduced. ●An effective necessary and sufficient stability criterion has been given for arbitrary FOS discrete-based systems. ●Using presented approach of calculating Lyapunov exponents (LEs) and also bifurcation diagrams, existence of (inverse) period-doubling route to chaos has been explored. ●Besides the role of growth rate parameter, the impact of fractional order and economic interest parameters on the chaotic zones has been demonstrated. - Abstract: Recently fractional calculus started to gain much importance due to its applications to the mathematical modeling of real phenomena with memory effect. Besides, singular modeling, which has been accompanied by exhibiting more complicated dynamics rather than standard models, can reveal the instability mechanism of wide-range of physical systems. Utilizing these two applicable techniques of modeling, a generalization of the logistic growth model, which takes into account the effects of memory and economic interest, is suggested in this paper. Besides mathematical analysis and extracting new results on the equilibrium points and local stability studies of discrete-time commensurate fractional-order singular (FOS) state space systems, some basic dynamical properties and qualitative analysis of the new chaotic FOS logistic map are studied, either numerically or analytically, to explore the impacts of real order and economic interest on the presented system in biological contexts.
[en] Highlights: • To understand the microstructure of pellets and improve the metallurgical properties of pellets, fractal theory is introduced to extract the edge features of pellets. • The original mineralogical phase is obtained by experiment, which is preprocessed by the histogram equalization to enhance the overall contrast. • Based on the discrete Fractional Brownian Random Field Model, the algorithm is redesigned to calculate the dimension of each pixel, map the gray space of image into the dimension space, select the appropriate window size, transform and edge detection. • Comparing the algorithm in this paper with Canny operator and Laplace–Gauss operator, it is concluded that the algorithm in this paper has certain advantages in mineralogical phase edge extraction. • Gauss noise is added to the original gray image, and Canny operator and this algorithm are used to extract the edges of the noisy image. • The numerical results of peak signal to noise ratio and root mean square error are obtained. Finally, • The comparison proves that the algorithm can extract more complete edges, and has a stronger noise immunity. - Abstract: In order to understand the microstructure of pellets and improve the metallurgical properties of pellets, fractal theory is introduced to extract the edge features of pellets. Firstly, the original mineralogical phase is obtained by experiment, which is preprocessed by the histogram equalization to enhance the overall contrast. Based on the discrete Fractional Brownian Random Field Model, the algorithm is redesigned to calculate the dimension of each pixel, map the gray space of image into the dimension space, select the appropriate window size, transform and edge extraction. Comparing the algorithm in this paper with Canny operator and Laplace–Gauss operator, it is concluded that the algorithm in this paper has certain advantages in mineralogical phase edge extraction. Then, Gauss noise is added to the original gray image, and Canny operator and this algorithm are used to extract the edges of the noisy image. The numerical results of peak signal to noise ratio and root mean square error are obtained. Finally, the comparison proves that the algorithm can extract more complete edges, and has a stronger noise immunity.
[en] Highlights: • Edges between individuals in the network are constructed by the attributes of users and items and rating scores converging forgetting function. • Differential equations are proposed to imitate the constantly changing states of the nodes in heterogeneous networks. • The predicted ratings are calculated in each subclass based on user collaborative filtering. - Abstract: Collaborative filtering is one of the most widely used individual recommendation algorithms. The traditional collaborative filtering recommendation algorithm takes less care of time variation, which may be inaccurate in real surroundings. A novel dynamic evolutionary clustering algorithm based on time weight and latent attributes is proposed. According to the time effect of historical information in recommendation system, forgetting curve is introduced to better grasp the recent interest of the users. To gather users with similar interest into the same cluster, item characteristics and user attributes are mined. Therefore, network model is established by introducing the forgetting function to score matrix, utilizing item characteristics and user attributes. Items and users are regarded as heterogenous nodes in network. Furthermore, a novel dynamic evolutionary clustering algorithm is adopted to divide users and items set into K clusters, and individuals with higher similarity are clustered. The preferences of users in the same cluster are similar. Then, collaborative filtering is applied in each cluster to predict the ratings. Finally, the target users are recommended predicted according to prediction ratings. Simulations show that the presented method gains better recommendation accuracy in comparison of existing algorithms through MovieLens100k, Restaurant & consumer and CiaoDVD data sets.
[en] Highlights: • Double-mean-reverting volatility is considered for variance swaps. • We obtain closed form exact solutions or approximations. • The characteristic function is exploited to derive the prices. • Numerical tests show the validity and sensitivity of the prices. - Abstract: A three factor variance model introduced by Gatheral in 2008, called the double mean reverting (DMR) model, is well-known to reflect the empirical dynamics of the variance and prices of options on both SPX and VIX consistently with the market. One drawback of the DMR model is that calibration may not be easy as no closed form solution for European options exists, not like the Heston model. In this paper, we still use the double mean reverting nature to extend the Heston model and study the pricing of variance swaps given by simple returns in discrete sampling times. The constant mean level of Heston’s stochastic volatility is extended to a slowly varying process which is specified in two different ways in terms of the Ornstein-Uhlenbeck (OU) and Cox-Ingersoll-Ross (CIR) processes. So, two types of double mean reversion are considered and the corresponding models are called the double mean reverting Heston-OU model and the double mean reverting Heston-CIR models. We solve Riccati type nonlinear equations and derive closed form exact solutions or closed form approximations of the fair strike prices of the variance swaps depending on the correlation structure of the three factors. We verify the accuracy of our analytic solutions by comparing with values computed by Monte Carlo simulation. The impact of the double mean reverting formulation on the fair strike prices of the variance swaps are also scrutinized in the paper.
[en] Highlights: • The fractional derivative was introduced into the modeling of generator. • The coupled bending-torsional vibration was considered in the model. • The stability of generator with the changes of system parameters was discussed. • Some critical values and ranges of system were proposed. ABSTRACTUnexpected vibrations induced by the crack fault and other unbalance factors in rotor system seriously affect the health and reliability of the generator. Here, to explore the vibration performances, a bending-torsional coupling model of the generator rotor shaft system is established, in which electromagnetic malfunction (unbalanced magnetic pull) and mechanical failures (fractional-order damping, crack and contact-rubbing) are considered. Then, the simulation is done by a modified Adams-Bashforth-Moulton algorithm. Based on the simulation, the correctness of the new coupling model is verified by comparing with previous model and experimental data. At the same time, the new coupling model is analyzed to obtain the dynamic evolutions of the generator rotor shaft system with the changes of crack depth ratio, the fractional order of damping, rotational speed ratio and mass eccentricity of rotor. In addition to this, some critical values and ranges are proposed. Finally, these results can efficiently provide a theoretical reference for the design of generator rotor system and be applied to forecasting and diagnosing vibration faults in generator rotor shaft system.
[en] In the present article coupled drift-ion acoustic mode is investigated in four component collisional, magnetized, and inhomogeneous ambiplasma consisting of positive and negative ions, non-thermal electrons and positrons. Linear dispersion relation for the coupled mode is derived with effect of nothermality and particle concentration. In the presence of weak dispersion and dissipation a KdV-Burger equation is derived in nonlinear regime, for coupled acoustic-drift shock and soliton. Using Tanh-method the solution for double layers in the system is derived. The results are numerically highlighted for ambi plasma at early universe and space plasma. Further more keeping in view the non thermal behavior of ambiplasma in space, a kappa distributed approach is used for these calculations.
[en] Highlights: • Combining with intermittent control method, we propose a fuzzy method to realize synchronization of chaotic system. • Based on the method, we establish two plant rules of intermittent control, and get a fuzzy synchronization scheme. • Finally, a simulation example is proposed to verify the effectiveness of our results. - Abstract: In this paper, a fuzzy method is combined with intermittent control method to realize synchronization of chaotic system. Two plant rules of intermittent control are considered to get two theorems. Fuzzy scheme for synchronization is proposed in theorem. Finally, a simulation example is proposed to verify the effectiveness of our results.
[en] Highlights: • Plasma chaotic system is transformed into a Kolmogorov type of system. • The vector field of the chaotic system is decomposed into four types of torques. • The dynamical modes of plasma relate to the combination of torques. • An analytical supremum bound of the plasma chaotic attractor is proposed. - Abstract: Plasma is normally investigated via fluid dynamics, and to investigate the force and energy underlying a plasma chaotic system, it is first transformed into a Kolmogorov-type system. This system describes a general form of fluid and forced-dissipative rigid body system. The vector field of the plasma chaotic system is decomposed into four types of torque: inertial torque, internal torque, dissipation, and external torque. The Hamiltonian energy transfer between kinetic energy and potential is discovered. The various combinations of these four types of torque are constructed to uncover the effect of each on the generation of the dynamic mode of the chaotic system. The physical functions of the whistler and dampening of the pump are identified in producing the different plasma dynamics. Aside from the torque effects, the rate of change of the Casimir function is also a key factor in characterizing the orbit behavior of the plasma system. Last, a supremum bound of the plasma chaotic attractor is proposed.
[en] Highlights: • Pattern self-organization in a reaction-convection-diffusion predator–prey system is investigated. • Two pattern transitions along the route to chaos are found corresponding to two initial conditions. • Alternation between ordered patterns and disordered chaos is revealed in the pattern transition. • Turing instability driven by convection and diffusion can force the transformation from homogeneous chaotic states to ordered striped patterns. - Abstract: This research investigates pattern self-organization along the route to chaos in a space- and time-discrete predator–prey system, where the prey shows convection movement in space. Through analysis on Turing instability of the system, pattern self-organization conditions are determined. Based on the conditions, simulations are performed under two initial conditions, demonstrating two pattern transitions along the route to chaos. In the first pattern transition, the patterns start from regular stripes, experiencing twisted stripes, then return to regular stripes again. The second pattern transition is much more complex and shows three stages. Especially, an alternation between ordered patterns and disordered chaos is found, contributing greatly to the spatiotemporal complexity of the system. When the system stays at the homogeneous chaotic states, Turing instability driven by convection and diffusion can still force the self-organization of regular striped patterns. The finding in this research provides a new comprehending for pattern self-organization and transition in spatially extended predator–prey systems.