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Abstract We study the synchronization properties of a generic networked dynamical system, and show that, under a suitable approximation, the transition to synchronization can be predicted with the only help of eigenvalues and eigenvectors of the graph Laplacian matrix. The transition comes out to be made of a well defined sequence of events, each of which corresponds to a specific clustered state. The network’s nodes involved in each of the clusters can be identified, and the value of the coupling strength at which the events are taking place can be approximately ascertained. Finally, we present large-scale simulations which show the accuracy of the approximation made, and of our predictions in describing the synchronization transition of both synthetic and real-world large size networks, and we even report that the observed sequence of clusters is preserved in heterogeneous networks made of slightly non-identical systems.

The master stability function is a robust and useful tool for determining the conditions of synchronization stability in a network of coupled systems. While a comprehensive classification exists in the case in which the nodes are chaotic dynamical systems, its application to periodic systems has been less explored. By studying several well-known periodic systems, we establish a comprehensive framework to understand and classify their properties of synchronizability. This allows us to define five distinct classes of synchronization stability, including some that are unique to periodic systems. Specifically, in periodic systems, the master stability function vanishes at the origin, and it can therefore display behavioral classes that are not achievable in chaotic systems, where it starts, instead, at a strictly positive value. Moreover, our results challenge the widely held belief that periodic systems are easily put in a stable synchronous state, showing, instead, the common occurrence of a lower threshold for synchronization stability.

The significance of discrete neural models lies in their mathematical simplicity and computational ease. This research focuses on enhancing a neural map model by incorporating a hyperbolic tangent-based memristor. The study extensively explores the impact of magnetic induction strength on the model's dynamics, analyzing bifurcation diagrams and the presence of multistability. Moreover, the investigation extends to the collective behavior of coupled memristive neural maps with electrical, chemical, and magnetic connections. The synchronization of these coupled memristive maps is examined, revealing that chemical coupling exhibits a broader synchronization area. Additionally, diverse chimera states and cluster synchronized states are identified and discussed.

Background and objectives: Endurance exercise causes fatigue due to mitochondrial dysfunction and oxidative stress. The present study was designed to investigate the effects of taurine supplementation on lipids peroxidation and antioxidant activity during endurance activities. Methods: Twenty-four male volunteers aged 27 ± 1.8 years and weighting 74.9 ± 5.9 kg were randomly divided into three groups: taurine supplementation (n=8), placebo (n=8), and control (n=8). The subjects completed a 28-day endurance training protocol. Biochemical parameters such as superoxide dismutase (SOD), glutathione peroxidase (GPX) activities, as well as malondialdehyde (MDA) concentrations (8 hours before the first session and 8 hours after the last session) and maximum rate of oxygen consumption, were measured to evaluate the antioxidant, lipid peroxidation, and VO2 max status respectively. Finally, data were analyzed by SPSS software at a significance level of

Human evolution is carried out by two genetic systems based on DNA and another based on the transmission of information through the functions of the nervous system. In computational neuroscience, mathematical neural models are used to describe the biological function of the brain. Discrete-time neural models have received particular attention due to their simple analysis and low computational costs. From the concept of neuroscience, discrete fractional order neuron models incorporate the memory in a dynamic model. This paper introduces the fractional order discrete Rulkov neuron map. The presented model is analyzed dynamically and also in terms of synchronization ability. First, the Rulkov neuron map is examined in terms of phase plane, bifurcation diagram, and Lyapunov exponent. The biological behaviors of the Rulkov neuron map, such as silence, bursting, and chaotic firing, also exist in its discrete fractional-order version. The bifurcation diagrams of the proposed model are investigated under the effect of the neuron model's parameters and the fractional order. The stability regions of the system are theoretically and numerically obtained, and it is shown that increasing the order of the fractional order decreases the stable areas. Finally, the synchronization behavior of two fractional-order models is investigated. The results represent that the fractional-order systems cannot reach complete synchronization.

Working memory has been identified as a top-down modulation of the average spiking activity in different brain parts. However, such modification has not yet been reported in the middle temporal (MT) cortex. A recent study showed that the dimensionality of the spiking activity of MT neurons increases after deployment of spatial working memory. This study is devoted to analyzing the ability of nonlinear and classical features to capture the content of the working memory from the spiking activity of MT neurons. The results suggest that only the Higuchi fractal dimension can be considered as a unique indicator of working memory while the Margaos-Sun fractal dimension, Shannon entropy, corrected conditional entropy, and skewness are perhaps indicators of other cognitive factors such as vigilance, awareness, and arousal as well as working memory.

Neural signatures of working memory have been frequently identified in the spiking activity of different brain areas. However, some studies reported no memory-related change in the spiking activity of the middle temporal (MT) area in the visual cortex. However, recently it was shown that the content of working memory is reflected as an increase in the dimensionality of the average spiking activity of the MT neurons. This study aimed to find the features that can reveal memory-related changes with the help of machine-learning algorithms. In this regard, different linear and nonlinear features were obtained from the neuronal spiking activity during the presence and absence of working memory. To select the optimum features, the Genetic algorithm, Particle Swarm Optimization, and Ant Colony Optimization methods were employed. The classification was performed using the Support Vector Machine (SVM) and the K-Nearest Neighbor (KNN) classifiers. Our results suggest that the deployment of spatial working memory can be perfectly detected from spiking patterns of MT neurons with an accuracy of 99.65±0.12 using the KNN and 99.50±0.26 using the SVM classifiers.

Simplicial complexes are mathematical constructions that describe higher-order interactions within the interconnecting elements of a network. Such higher-order interactions become increasingly significant in neuronal networks since biological backgrounds and previous outcomes back them. In light of this, the current research explores a higher-order network of the memristive Rulkov model. To that end, the master stability functions are used to evaluate the synchronization of a network with pure pairwise hybrid (electrical and chemical) synapses alongside a network with two-node electrical and multi-node chemical connections. The findings provide good insight into the impact of incorporating higher-order interaction in a network. Compared to two-node chemical synapses, higher-order interactions adjust the synchronization patterns to lower multi-node chemical coupling parameter values. Furthermore, the effect of altering higher-order coupling parameter value on the dynamics of neurons in the synchronization state is researched. It is also shown how increasing network size can enhance synchronization by lowering the value of coupling parameters whereby synchronization occurs. Except for complete synchronization, cluster synchronization is detected for higher electrical coupling strength values wherein the neurons are out of the completed synchronization state.

This paper presents a study on a memristive two-neuron-based Hopfield neural network with fractional-order derivatives. The equilibrium points of the system are identified, and their stability is analyzed. Bifurcation diagrams are obtained by varying the magnetic induction strength and the fractional-order derivative, revealing significant changes in the system dynamics. It is observed that lower fractional orders result in an extended bistability region. Also, chaos is only observed for larger magnetic strengths and fractional orders. Additionally, the application of the fractional-order model for image encryption is explored. The results demonstrate that the encryption based on the fractional model is efficient with high key sensitivity. It leads to an encrypted image with high entropy, neglectable correlation coefficient, and uniform distribution. Furthermore, the encryption system shows resistance to differential attacks, cropping attacks, and noise pollution. The Peak Signal-to-Noise Ratio (PSNR) calculations indicate that using a fractional derivative yields a higher PSNR compared to an integer derivative.

Studying simple chaotic systems with fractional-order derivatives improves modeling accuracy, increases complexity, and enhances control capabilities and robustness against noise. This paper investigates the dynamics of the simple Sprott-B chaotic system using fractional-order derivatives. This study involves a comprehensive dynamical analysis conducted through bifurcation diagrams, revealing the presence of coexisting attractors. Additionally, the synchronization behavior of the system is examined for various derivative orders. Finally, the integer-order and fractional-order electronic circuits are implemented to validate the theoretical findings. This research contributes to a deeper understanding of the Sprott-B system and its fractional-order dynamics, with potential applications in diverse fields such as chaos-based secure communications and nonlinear control systems.

The Rulkov map model is an efficient model for reproducing different dynamics of the neurons. In specific neurons, the electrical activity is regulated by time-delayed self-feedback called autapse. This paper investigates how the dynamics of the Rulkov model change by considering the autaptic current. Both electrical and chemical autapses are considered, and bifurcation diagrams are plotted for different autapse gains and time delays. Consequently, various firing patterns of the model are illustrated. The results represent that the firing pattern is greatly dependent on the values of autapse parameters. Moreover, the average firing frequency is computed and it is shown that the enhanced firing activity is induced by the inhibitory autapse. The synchronous dynamics of coupled Rulkov maps in the presence of autapse is also studied. It is shown that the electrical autapse enhances synchronization in small time delays, while the enhancement is achieved by chemical autapse in any time delay. However, increasing the time delay reduces the synchronization region.

One of the famous economic models in game theory is the duopoly Stackelberg model, in which a leader and a follower firm manufacture a single product in the market. Their goal is to obtain the maximum profit while competing with each other. The desired dynamics for a firm in a market is the convergence to its Nash equilibrium, but the dynamics of real-world markets are not always steady and can result in unpredictable market changes that exhibit chaotic behaviors. On the other hand, to approach reality more, the two firms in the market can be considered heterogeneous. The leader firm is bounded rationale, and the follower firm is adaptable. Modifying the cost function that affects the firms' profit by adding the marginal cost term is another step toward reality. We propose a Stackelberg model with heterogeneous players and marginal costs, which exhibits chaotic behavior. This model's equilibrium points, including the Nash equilibrium, are calculated by the backward induction method, and their stability analyses are obtained. The influence of changing each model parameter on the consequent dynamics is investigated through one-dimensional and two-dimensional bifurcation diagrams, Lyapunov exponents spectra, and Kaplan-Yorke dimension. Eventually, using a combination of state feedback and parameter adjustment methods, the chaotic solutions of the model are successfully tamed, and the model converges to its Nash equilibrium.

Although Iran is a developing country, social responsibility has not yet found a strong footing in Iranian organizations and companies. Hence, this study aimed at designing a social responsibility pyramid at Social Security Organization from its stakeholders’ perspective. To this end, an open-ended analytic interview was conducted with 20 experts at different levels whose views were analyzed using a thematic approach in MaxQDA software version 12. Further, the relationships among themes initially identified in the qualitative stage were determined via Interpretive Structural Modelling and using manual calculations and Excel Software. The findings from the designed social responsibility pyramid indicated service improvement and voluntary optional activities as the first level variables, economic and financial activities as those of the second level, political activities, education and research as the third level and finally regulations, organizational components and organizational culture as the fourth level variables. The study underscores the new insights that can be drawn from a constructive phenomenological approach about social responsibility in the specific context of the social security organization and can offer implications for its stakeholders.

Map-based neuronal models have received much attention due to their high speed, efficiency, flexibility, and simplicity. Therefore, they are suitable for investigating different dynamical behaviors in neuronal networks, which is one of the recent hottest topics. Recently, the memristive version of the Rulkov model, known as the m-Rulkov model, has been introduced. This paper investigates the network of the memristive version of the Rulkov neuron map to study the effect of the memristor on collective behaviors. Firstly, two m-Rulkov neuronal models are coupled in different cases, through electrical synapses, chemical synapses, and both electrical and chemical synapses. The results show that two electrically coupled memristive neurons can become synchronous, while the previous studies have shown that two non-memristive Rulkov neurons do not synchronize when they are coupled electrically. In contrast, chemical coupling does not lead to synchronization; instead, two neurons reach the same resting state. However, the presence of both types of couplings results in synchronization. The same investigations are carried out for a network of 100 m-Rulkov models locating in a ring topology. Different firing patterns, such as synchronization, lagged-phase synchronization, amplitude death, non-stationary chimera state, and traveling chimera state, are observed for various electrical and chemical coupling strengths. Furthermore, the synchronization of neurons in the electrical coupling relies on the network's size and disappears with increasing the nodes number.

In network analysis, links depict the connections between each pair of network nodes. However, such pairwise connections fail to consider the interactions among more agents, which may be indirectly connected. Such non-pairwise or higher-order connections can be signified by involving simplicial complexes. The higher-order connections become even more noteworthy when it comes to neuronal network synchronization, an emerging phenomenon responsible for the many biological processes in real-world phenomena. However, involving higher-order interactions may considerably increase the computational costs. To confound this issue, map-based models are more suitable since they are faster, simpler, more flexible, and computationally more optimal. Therefore, this paper addresses the impact of pairwise and non-pairwise neuronal interactions on the synchronization state of 10 coupled memristive Hindmarsh–Rose neuron maps. To this aim, electrical, inner linking, and chemical synaptic functions are considered as two- and three-body interactions in three homogeneous and two heterogeneous cases. The results show that through chemical pairwise and non-pairwise synapses, the neurons achieve synchrony with the weakest coupling strengths.

Memristor is a non-linear circuit element in which voltage-current relationship is determined by the previous values of the voltage and current, generally the history of the circuit. The nonlinearity in this component can be considered as a fractional-order form, which yields a fractional memristor (fracmemristor). In this paper, a fractional-order memristor in a chaotic oscillator is applied, while the other electronic elements are of integer order. The fractional-order range is determined in a way that the circuit has chaotic solutions. Also, the statistical and dynamical features of this circuit are analyzed. Tools like Lyapunov exponents and bifurcation diagram show the existence of multistability and antimonotonicity, two less common properties in chaotic circuits.

In this paper, a new jerk system is designed. This system can display different characters of equilibrium points according to the value of its parameters. The proposed nonlinear oscillator can have both self-excited and hidden attractors. Dynamical properties of this system are investigated with the help of eigenvalues of equilibria, Lyapunov exponents' spectrum, and bifurcation diagrams. Also, an electronic circuit implementation is carried out to show the feasibility of this system. As an engineering application of this new chaotic jerk system, a chaotic communication system is realized by correlation delay shift keying. When the results of the communication system are examined, the transmitted information signal is successfully obtained in the receiving unit, and its performance efficiency is investigated in the presence of additive white Gaussian noise.

This work introduces a three-dimensional, highly nonlinear quadratic oscillator with no linear terms in its equations. Most of the quadratic ordinary differential equations (ODEs) such as Chen, Rossler, and Lorenz have at least one linear term in their equations. Very few quadratic systems have been introduced and all of their terms are nonlinear. Considering this point, a new quadratic system with no linear term is introduced. This oscillator is analyzed by mathematical tools such as bifurcation and Lyapunov exponent diagrams. It is revealed that this system can generate different behaviors such as limit cycle, torus, and chaos for its different parameters’ sets. Besides, the basins of attractions for this system are investigated. As a result, it is revealed that this system’s attractor is self-excited. In addition, the analog circuit of this oscillator is designed and analyzed to assess the feasibility of the system’s chaotic solution. The PSpice simulations confirm the theoretical analysis. The oscillator’s time series complexity is also investigated using sample entropy. It is revealed that this system can generate dynamics with different sample entropies by changing parameters. Finally, impulsive control is applied to the system to represent a possible solution for stabilizing the system.

In this paper, a chaotification method based on the internal perturbation model (IPM) is proposed. The single-perturbation and the multiple-perturbations are introduced. The Sine map is taken as an example. Moreover, this method can be generalized to high-dimensional maps that contain sine, no matter where the sine term is in the system equation. we further apply IPM to an integer-order and a fractional-order Sine-series map. For those new maps, the parameter space and FuzzyEn complexity are significantly extended while maintaining the topological structure of system. These complex behaviors and digital signal processing (DSP) implementation validate the effectiveness of IPM and make it have the potential of better secure communication and encryption.

The dynamical interplay of coupled non-identical chaotic oscillators gives rise to diverse scenarios. The incoherent dynamics of these oscillators lead to the structural impairment of attractors in phase space. This paper investigates the couplings of Lorenz–Rössler, Lorenz–HR, and Rössler–HR to identify the dominant attractor. By dominant attractor, we mean the attractor that is less changed by coupling. For comparison and similarity detection, a cost function based on the return map of the coupled systems is used. The possible effects of frequency and amplitude differences between the systems on the results are also examined. Finally, the inherent chaotic characteristic of systems is compared by computing the largest Lyapunov exponent. The results suggest that in each coupling case, the attractor with the greater largest Lyapunov exponent is dominant.

Fractal dimension (FD) together with advances in imaging technologies has provided an increasing application of digital images to interpret biological phenomena. In ophthalmology, topography-based images are increasingly used in common practices of clinical settings. They provide detailed information about corneal surfaces. Few-micron alterations of the corneal geometry to the elevation and curvature cause a highly multifocal surface, change the corneal optical power up to several diopters, and therefore adversely affect the individual’s vision. Keratoconus (KCN) is a corneal disease characterized by a local alteration of the corneal anatomical and mechanical features. The formation of cone-shaped regions accompanied by thinning and weakening of the cornea are the major manifestations of KCN. The implantation of tiny arc-like polymeric sections, known as intracorneal implants, is considered to be effective in restoring the corneal curvature. This study investigated the FD nature of healthy corneas (n = 7) and compared it to the corresponding values before and after intracorneal implant surgery in KCN patients (n = 7). The generalized Hurst exponent, Higuchi, and Katz FDs were computed for topography-based parameters of corneal surfaces: front elevation (ELE-front), back elevation (ELE-back), and corneal curvature (CURV). The Katz FD showed better discriminating ability for the diseased group. It could reveal a significant difference between the healthy corneas and both pre- and post-implantation topographies (p < 0.001). Moreover, the Katz dimension varied between the topographic features of KCN patients before and after the treatment (p < 0.036). We propose to describe the curvature feature of corneal topography as a “strange attractor” with a self-similar (i.e., fractal) structure according to the Katz algorithm.

There have been many different investigations of nonlinear dynamical systems. In this paper, we introduce a new chaotic system. In the proposed system, the attractor can be modified by adding a nonlinear term to the third state equation, thereby generating six different self-excited chaotic attractors. Some dynamical properties such as Hopf bifurcation, bifurcation diagrams, and multistability of the proposed system are investigated. The new system shows topologically different attractors for all six cases. We investigate two cases in depth. We also use nonlinear feedback control to drive the system to equilibrium, using two cases for illustration.

Recently, megastable systems have grabbed many researchers’ interests in the area of nonlinear dynamics and chaotic systems. In this paper, the oscillatory terms’ coefficients of the simplest megastable oscillator are forced to blink in time. The forced system can generate an infinitive number of hidden attractors without changing parameters. The behavior of these hidden attractors can be chaotic, tori, and limit cycle. The attractors’ topology of the system seems unique and looks like picture frames. Besides, the existence of different coexisting attractors with different kinds of behaviors reflects the system's high sensitivity. Using the sample entropy algorithm, the system’s complexity for different initial values is assessed. In addition, the circuit of the introduced forced system is designed, and the possibility of implicating the system with analog elements is investigated.

Designing chaotic systems with different properties helps to increase our knowledge about real-world chaotic systems. In this article, a piecewise linear (PWL) term is employed to modify a simple chaotic system and obtain a new chaotic model. The proposed model does not have any equilibrium for different values of the control parameters. Therefore, its attractor is hidden. It is shown that the PWL term causes an offset boostable variable. This feature provides more flexibility and controllability in the designed system. Numerical analyses show that periodic and chaotic attractors coexist in some fixed values of the parameters, indicating multistability. Also, the feasibility of the system is approved by designing field programmable gate arrays (FPGA).

Megastable chaotic systems are somehow the newest in the family of special chaotic systems. In this paper, a new megastable two-dimensional system is proposed. In this system, coexisting attractors are in some islands, interestingly covered by megalimit cycles. The introduced two-dimensional system has no defined equilibrium point. However, it seems that the origin plays the role of an unstable equilibrium point. Therefore, the attractors are determined as hidden attractors. Adding a forcing term to the system, we can obtain chaotic solutions and coexisting strange attractors. Moreover, the effect of three different values of the forcing term’s amplitude is studied. The dynamical properties of the designed system are investigated using attractor plots, bifurcation diagrams, and Lyapunov Exponents diagram. Phase portraits of the novel megastable oscillator are presented by FPGA design. Xilinx system generator block diagrams of the proposed system and trigonometric functions are also presented.

In this paper, bifurcation points of two chaotic maps are studied: symmetric sine map and Gaussian map. Investigating the properties of these maps shows that they have a variety of dynamical solutions by changing the bifurcation parameter. Sine map has symmetry with respect to the origin, which causes multistability in its dynamics. The systems’ bifurcation diagrams show various dynamics and bifurcation points. Predicting bifurcation points of dynamical systems is vital. Any bifurcation can cause a huge wanted/unwanted change in the states of a system. Thus, their predictions are essential in order to be prepared for the changes. Here, the systems’ bifurcations are studied using three indicators of critical slowing down: modified autocorrelation method, modified variance method, and Lyapunov exponent. The results present the efficiency of these indicators in predicting bifurcation points.

The fractional calculus in the neuronal models provides the memory properties. In the fractional-order neuronal model, the dynamics of the neuron depends on the derivative order, which can produce various types of memory-dependent dynamics. In this paper, the behaviors of the coupled fractional-order FitzHugh–Nagumo neurons are investigated. The effects of the coupling strength and the derivative order are under consideration. It is revealed that the level of the synchronization is decreased by decreasing the derivative order, and the chimera state emerges for stronger couplings. Furthermore, the patterns of the formed chimeras rely on the order of the derivatives.

Studying new chaotic flows with specific characteristics has been an open-ended field of exploring nonlinear dynamics. Investigation of chaotic flows is an area of research that has been taken into consideration for many years; thus, it helps in a better understanding of the chaotic systems. In this paper, an original chaotic 3D system, which has not been investigated yet, is presented in spherical coordinates. A unique feature of the proposed system is that its velocity becomes zero for a specific value of the radius variable. Hence, the system’s attractor is expected to be stuck on one side of a plane in spherical coordinates and inside or outside a sphere in the corresponding Cartesian coordinates. It means that the attractor cannot pass through the sphere or even touch it. The introduced system owns two unstable equilibria and a self-excited strange attractor. The 1D and 2D system’s bifurcation diagrams concerning the alteration of two bifurcation parameters are plotted to investigate the system’s dynamical properties. Moreover, the system’s Lyapunov exponents in the corresponding period of bifurcation parameters are calculated. Then, two 2D basins of attraction for two different third dimension values are explored. Based on the basin of attraction, it can be found that the sphere has attraction itself, partially, and some initial conditions are led to the sphere, not to the strange attractor. Ultimately, the connecting curves of the proposed system are explored to find an informative 1D set in addition to the system’s equilibria.

Fractional-order neuronal models that include memory effects can describe the rich dynamics of the firing of the neurons. This paper studies synchronization problems in a multiple network of Caputo–Fabrizio type fractional order neurons in which the orders of the derivatives in the layers are different. It is observed that the intralayer synchronization state occurs in weaker intralayer couplings when using nonidentical fractional-order derivatives rather than integer-order or identical fractional orders. Furthermore, the needed interlayer coupling strength for interlayer near synchronization decreases for lower fractional orders. The dynamics of the neurons in nonidentical layers are also considered. It is shown that in lower fractional orders, the neurons’ dynamics change to periodic when the near synchronization state occurs. Moreover, decreasing the derivative order leads to incrementing the frequency of the bursts in the synchronization manifold, which is in contrast to the behavior of the single neuron.

The fundamental dynamics of the deformed Rikitake two-disc dynamo system is explored in this paper. Memory effect on the dynamical behavior of the generator system is studied by introducing a quadratic flux-controlled memristor. Hyperchaotic oscillation in the deformed Rikitake two-disk coupled generator is therefore firstly found. Lyapunov exponents, bifurcation diagram, and phase portraits prove the abundant dynamic behavior consistently.

The dimension of the conservative chaotic systems is an integer and equals the system dimension, which brings about a better ergodic property and thus have potentials in engineering application than the dissipative systems. This paper investigates the phenomenon of megastability in a unique and simple conservative oscillator with infinite of hyperbolic and nonhyperbolic equilibria. Using traditional nonlinear analysis tools, we found that the introduced oscillator possesses an invariable energy and displays either self-excited or hidden dynamics depending on the stability of its equilibria. Besides, the conservative nature of the new system is validated using theoretical measurement. Furthermore, an analog simulator of the oscillator is built and simulated in the PSpice environment to confirm that the previous results were not artifacts.

Here, a chaotic quadratic oscillator with only squared terms is proposed, which shows various dynamics. The oscillator has eight equilibrium points, and none of them is stable. Various bifurcation diagrams of the oscillator are investigated, and its Lyapunov exponents (LEs) are discussed. The multistability of the oscillator is discussed by plotting bifurcation diagrams with various initiation methods. The basin of attraction of the oscillator is discussed in two planes. Impulsive control is applied to the oscillator to control its chaotic dynamics. Additionally, the circuit is implemented to reveal its feasibility.

Multimedia data play an important role in our daily lives. The evolution of internet technologies means that multimedia data can easily participate amongst various users for specific purposes, in which multimedia data confidentiality and integrity have serious security issues. Chaos models play an important role in designing robust multimedia data cryptosystems. In this paper, a novel chaotic oscillator is presented. The oscillator has a particular property in which the chaotic dynamics are around pre-located manifolds. Various dynamics of the oscillator are studied. After analyzing the complex dynamics of the oscillator, it is applied to designing a new image cryptosystem, in which the results of the presented cryptosystem are tested from various viewpoints such as randomness, time encryption, correlation, plain image sensitivity, key-space, key sensitivity, histogram, entropy, resistance to classical types of attacks, and data loss analyses. The goal of the paper is proposing an applicable encryption method based on a novel chaotic oscillator with an attractor around a pre-located manifold. All the investigations confirm the reliability of using the presented cryptosystem for various IoT applications from image capture to use it.

Recently, systems with chaos and the absence of equilibria have received a great deal of attention. In our work, a simple five-term system and its anti-synchronization are presented. It is special that the system has a hyperbolic sine nonlinearity and no equilibrium. Such a system generates chaotic behaviours, which are verified by phase portraits, positive Lyapunov exponent as well as an electronic circuit. Moreover, the system displays multistable characteristic when changing its initial conditions. By constructing an adaptive control, chaos anti-synchronization of the system with no equilibrium is obtained and illustrated via a numerical example.

A fundamental understanding and simulation of fuel atomization, phase transition, and mixing are among the topics researchers have struggled with for decades. One of the reasons for this is that the accurate, robust, and efficient simulation of fuel jets remains a challenge. In this paper, a tabulated multi-component real-fluid model (RFM) is proposed to overcome most of the limitations and to make real-fluid simulations affordable. Essentially, a fully compressible two-phase flow and a diffuse interface approach are used for the RFM model, which were implemented in the CONVERGE solver. PISO and SIMPLE numerical schemes were modified to account for a highly coupled real-fluid tabulation approach. These new RFM model and numerical schemes were applied to the simulation of different fundamental 1-D, 2-D, and 3-D test cases to better understand the structure of subcritical and transcritical liquid–gas interfaces and to reveal the hydro-thermodynamic characteristics of multicomponent jet mixing. The simulation of a classical cryogenic injection of liquid nitrogen coaxially with a hot hydrogen jet is performed using thermodynamic tables generated by two different equations of state: Peng–Robinson (PR) and Soave–Redlich–Kwong (SRK). The numerical results are finally compared with available experimental data and published numerical studies with satisfactory agreement.

In this paper, the stabilization and synchronization of a complex hidden chaotic attractor is shown. This article begins with the dynamic analysis of a complex Lorenz chaotic system considering the vector field properties of the analyzed system in the Cn domain. Then, considering first the original domain of attraction of the complex Lorenz chaotic system in the equilibrium point, by using the required set topology of this domain of attraction, one hidden chaotic attractor is found by finding the intersection of two sets in which two of the parameters, r and b, can be varied in order to find hidden chaotic attractors. Then, a backstepping controller is derived by selecting extra state variables and establishing the required Lyapunov functionals in a recursive methodology. For the control synchronization law, a similar procedure is implemented, but this time, taking into consideration the error variable which comprise the difference of the response system and drive system, to synchronize the response system with the original drive system which is the original complex Lorenz system.

Recent evidences suggest that complex behavior such as chaos can be observed in a nonlinear system with stable equilibria. However, few studies have investigated chaotic systems with only one stable equilibrium. This paper introduces a new 3-D chaotic system having only one stable equilibrium. Dynamics of the new system are discovered by using phase portraits, basin of attraction, bifurcation diagram, and maximal Lyapunov exponents. It is interesting that the system has a state variable related with the freedom of offset boosting. In addition, we have investigated the anti-synchronization of the system via an adaptive control. Furthermore, the feasibility of the system is also discussed through presenting its electronic circuit implementation.

According to the pioneering work of Leonov and Kuznetsov [...]

A modification of the classic logistic map is proposed, using fuzzy triangular numbers. The resulting map is analysed through its Lyapunov exponent (LE) and bifurcation diagrams. It shows higher complexity compared to the classic logistic map and showcases phenomena, like antimonotonicity and crisis. The map is then applied to the problem of pseudo random bit generation, using a simple rule to generate the bit sequence. The resulting random bit generator (RBG) successfully passes the National Institute of Standards and Technology (NIST) statistical tests, and it is then successfully applied to the problem of image encryption.

A rare three-dimensional chaotic system with all eigenvalues equal to zero is proposed, and its dynamical properties are investigated. The chaotic system has one equilibrium point at the origin. Numerical analysis shows that the equilibrium point is unstable. Bifurcation analysis of the system shows various dynamics in a period-doubling route to chaos. We highlight that from the evaluation of the entropy, bifurcation points can be predicted by identifying early warning signals. In this manner, bifurcation points of the system are analyzed using Shannon and Kolmogorov-Sinai entropy. The results are compared with Lyapunov exponents.

Although many mathematical models have been presented for glucose and insulin interaction, none of these models can describe diabetes disease completely. In this work, the dynamical behavior of a regulatory system of glucose-insulin incorporating time delay is studied and a new property of the presented model is revealed. This property can describe the diabetes disease better and therefore may help us in deeper understanding of diabetes, interactions between glucose and insulin, and possible cures for this widespread disease.

Complexity is the undeniable part of the natural systems providing them with unique and wonderful capabilities. Memristor is known to be a fundamental block to generate complex behaviors. It also is reported to be able to emulate synaptic long-term plasticity as well as short-term plasticity. Synaptic plasticity is one of the important foundations of learning and memory as the high-order functional properties of the brain. In this study, it is shown that memristive neuronal network can represent plasticity phenomena observed in biological cortical synapses. A network of neuronal units as a two-dimensional excitable tissue is designed with 3-neuron Hopfield neuronal model for the local dynamics of each unit. The results show that the lattice supports spatiotemporal pattern formation without supervision. It is found that memristor-type coupling is more noticeable against resistor-type coupling, while determining the excitable tissue switch over different complex behaviors. The stability of the resulting spatiotemporal patterns against noise is studied as well. Finally, the bifurcation analysis is carried out for variation of memristor effect. Our study reveals that the spatiotemporal electrical activity of the tissue concurs with the bifurcation analysis. It is shown that the memristor coupling intensities, by which the system undergoes periodic behavior, prevent the tissue from holding wave propagation. Besides, the chaotic behavior in bifurcation diagram corresponds to turbulent spatiotemporal behavior of the tissue. Moreover, we found that the excitable media are very sensitive to noise impact when the neurons are set close to their bifurcation point, so that the respective spatiotemporal pattern is not stable.

In the last few years, entropy has been a fundamental and essential concept in information theory [...]

Chaotic systems without equilibrium are of interest because they are the systems with hidden attractors. A nonequilibrium system with chaos is introduced in this work. Chaotic behavior of the system is verified by phase portraits, Lyapunov exponents, and entropy. We have implemented a real electronic circuit of the system and reported experimental results. By using this new chaotic system, we have constructed S-boxes which are applied to propose a novel image encryption algorithm. In the designed encryption algorithm, three S-boxes with strong cryptographic properties are used for the sub-byte operation. Particularly, the S-box for the sub-byte process is selected randomly. In addition, performance analyses of S-boxes and security analyses of the encryption processes have been presented.

مقدمه: لازمه پیاده‌سازی فن‌آوری پزشکی از راه دور برای ارائه خدمات پزشکی و بهداشتی پذیرش آن است. هدف کلی مطالعه حاضر شناسایی عوامل مؤثر بر پذیرش پزشکی از راه دور با بهره‌گیری از فن‌آوری اطلاعات و ارتباطات بود. روش بررسی: روش این پژوهش تحلیلی و ابزار گردآوری اطلاعات آن، ترکیبی از پرسشنامه‌ی مدل پذیرش فن‌آوری و تئوری رفتار برنامه‌ریزی شده بود. جامعه‌ی آماری پژوهش حاضر پزشکان بیمارستان‌های شهر اصفهان در دوره‌ی زمانی اردیبهشت و تیر 1391 بودند که با استفاده از روش نمونه‌گیری تصادفی طبقه‌بندی شده، 125 نفر از آنان به عنوان نمونه‌ی پژوهش مورد بررسی قرار گرفتند. جهت سنجش روایی و پایایی مدل از روش مدل‌یابی معادلات ساختاری و آلفای کرونباخ استفاده شد و براساس نتایج تحلیل مسیر ارتباط متغیرهای این پژوهش مورد تأیید قرار گرفت. تجزیه و تحلیل داده‌ها با استفاده از نرم‌افزار SPSS19 و AMOS20 انجام شد. یافته‌ها: سودمندی درک شده (54/0=β) و سهولت درک شده (43/0=β) بر نگرش نسبت به استفاده از پزشکی از راه دور تأثیرگذار بودند. یافته‌های پژوهش همچنین حاکی از تأثیر مثبت سودمندی درک شده (61/0=β) و کنترل رفتاری درک شده (39/0=β) بر تمایل افراد نسبت به این نوع فن‌آوری بود، درحالی که هنجارهای ذهنی (18/0=β) بر تمایلات رفتاری مورد تأیید قرار نگرفت. نتیجه‌گیری: نتایج بدست آمده حاکی از این است که مدل پذیرش فن‌آوری و تئوری رفتار برنامه‌ریزی شده می‌تواند نیت افراد را در به‌کارگیری فن‌آوری پزشکی از راه دور پیش‌بینی نماید. واژه‌های کلیدی: پزشکی از راه دور؛ فن‌آوری؛ مراقبت سلامت؛ بیمارستان‌ها

Introduction: Whilst there is an extensive descriptive literature on the effective lecturing, there are few studies on students' perspective toward the attributes of effective lecture sessions. The aim of this study is to explore students' viewpoints on factors affecting the quality of lecture sessions. Methods: This was a two-stage descriptive study in which 25 dentistry students at clinical stage, studying at Tehran University of Medical Sciences attended a focus group session and represented their viewpoints about weaknesses and strengths of lecture sessions of theory courses. A questionnaire was developed according to the students’ statements. Features of an effective lecture session were categorized into 4 groups of factors related to the lecturer, content, physical facilities available in class, and educational management. Reliability was assessed through Spearman correlation analysis. This questionnaire including 45 items was distributed among 130 students studying at fourth to sixth-year, in the School of Dentistry. Students’ agreement with each item in questionnaire was measured using 5-point Likert scale. Results: Ninety seven questionnaires were collected. Items of factors related to the lecturer mostly regarded by students, among them were “oral presentation techniques” (mean score of 4.64), “presenting case to demonstrate the association between theory and practice” (4.63), and “the lecturer’s ability to associate the content” (4.55) which received the highest scores. Conclusion: Dentistry students at clinical stage thought that the role of lecture in theoretical courses is very important. They believed that the ability of lecturer in organizing and explanation of the content plays the most important role in giving an effective lecture.

Designing a chaotic system with infinitely many attractors is a hot topic. In this paper, multiscale multivariate permutation entropy (MMPE) and multiscale multivariate Lempel–Ziv complexity (MMLZC) are employed to analyze the complexity of those self-reproducing chaotic systems with one-directional and two-directional infinitely many chaotic attractors. The analysis results show that complexity of this class of chaotic systems is determined by the initial conditions. Meanwhile, the values of MMPE are independent of the scale factor, which is different from the algorithm of MMLZC. The analysis proposed here is helpful as a reference for the application of the self-reproducing systems.