Search

In this study, the higher order interactions, which are complex interactions involving more than two neurons, are studied in two real-world networks. These interactions play a crucial role in the brain's functioning, as they can influence the network's synchronization and dynamics. This paper analyzes the application of directed simplicial complexes, the mathematical realization of the higher order interactions, to study the synchronization of two Macaque rhesus brain networks. Interestingly, the directionally allows for the consideration of different simplicial motifs. The Hindmarsh–Rose chaotic system has been used to model the node dynamics. Also, electrical and chemical couplings are considered to be the interaction mechanism. The findings from this study provide valuable insights into the complex dynamics of brain networks. [ABSTRACT FROM AUTHOR]

The Lozi map is well-known and has been studied in various researches. By combining three research trends (discrete map, memristor and fractional calculus) we investigate a fractional memristive Lozi map in this work. Firstly the Grunwald–Letnikov fractional difference operator is used to introduce the new fractional map with no equilibrium point. Then, the coexistence of several chaotic hidden attractors is shown, along with the coexistence of a number of bifurcations, depending on the values of the initial conditions. We found attractive dynamics and characteristics of this fractional Lozi map. The realization with hardware platform illustrates the map's feasibility. [ABSTRACT FROM AUTHOR]

The use of the advancements in memristor technology to construct chaotic maps has garnered significant research attention in recent years. The combination of memristors and nonlinear terms provides an effective approach to proposing novel maps. In this study, we have leveraged memristors and sine terms to develop three-dimensional maps, capable of processing special fixed points. Additionally, we have conducted an in depth study of a specific example (TDMM 1 map) to demonstrate its dynamics, feasibility, and application for lightweight encryption. Notably, our general approach could be extended to develop higher-dimensional maps, including four- and five-dimensional ones, thereby opening up the possibility to create numerous higher-dimensional maps. [ABSTRACT FROM AUTHOR]

A memristor is a two-terminal passive electronic device that exhibits memory of resistance. It is essentially a resistor with memory, hence the name "memristor". The unique property of memristors makes them useful in a wide range of applications, such as memory storage, neuromorphic computing, reconfigurable logic circuits, and especially chaotic systems. Fixed point-free maps or maps without fixed points, which are different from normal maps due to the absence of fixed points, have been explored recently. This work proposes an approach to build fixed point-free maps by connecting a cosine term and a memristor. Four new fixed point-free maps displaying chaos are reported to illustrate this approach. The dynamics of the proposed maps are verified by iterative plots, bifurcation diagram, and Lyapunov exponents. Because such chaotic maps are highly sensitive to the initial conditions and parameter variations, they are suitable for developing novel lightweight random number generators. [ABSTRACT FROM AUTHOR]

In this study, an acidic (A) and pH-neutral (pHN) solution using poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) as the hole-transport layer (HTL) was modified using a 1-butyl-3-methylimidazolium chloride (BMIM+Cl−) ionic liquid (IL). The effects of this ionic liquid on the conductivity and morphological properties of the PEDOT:PSS films were investigated. The conductivity and morphological properties of the PEDOT: PSS films before and after adding IL were measured using a UV–vis spectrophotometer and atomic force microscope (AFM), respectively. The conductivity of the A-PEDOT:PSS-film-based ionic liquid was decreased, while the conductivity of the pHN-PEDOT:PSS-film-based ionic liquid was increased. The surface morphology of the A-PEDOT:PSS-film-based ionic liquid was slightly decreased, while the conductivity of the pHN-PEDOT:PSS-film-based ionic liquid was slightly increased. The vacuum-free planar hybrid solar cells (VFPHSCs) using the pHN-PEDOT:PSS-film-based ionic liquid show a higher power conversion efficiency (PCE) than the VFPHSCs using the A-PEDOT:PSS-film-based ionic liquid. We also report that a solar cell with a structure of ITO/pHN-PEDOT:PSS/PTB7:PCBM/PEO/EGaIn has a maximum PCE of about ~5%. [ABSTRACT FROM AUTHOR]

The dynamics of coupled chaotic circuits have particular importance in many applications. The Chua circuit is a well-known chaotic circuit that has been applied in various studies. In this paper, we investigate the network of Chua circuits in different coupling schemes. We consider three cases where the circuits are coupled through resistors, memristors, and inductors. The synchronization behavior of the network is examined for each case. It is observed that the nonstationary chimera is formed in coupled circuits in all coupling schemes. Complete synchronization can be achieved only in resistive coupling. In memristive coupled circuits, increasing the coupling strength leads to the instability of the network, while in the inductor coupling, the synchronization appears only among two variables, and the third variable cannot be synchronized. [ABSTRACT FROM AUTHOR]

The memristor, a specialized circuit element, has found recent applications in various areas. The nonlinearity of memristors can be harnessed to construct memristive maps, capable of generating complex behavior. In this paper, we present a model of a memristive map that incorporates two memristors, two amplifiers, and a control component. The proposed model allows for adjustments not only in the number of fixed points but also in the symmetry of the memristor map. As a result, the map exhibits diverse features, including chaos, a plane of fixed points, absence of fixed points, as well as symmetry and asymmetry, which can be controlled through modifications to the control component. To facilitate quick implementation and testing of the introduced map, we employed a cost-effective microcontroller board. The experimental results demonstrate the feasibility of the map and its potential for utilization in chaos-based applications. Furthermore, the proposed model opens the door to the creation of novel memristive maps. • A simple approach to construct two-memristor based maps is proposed. • Complex dynamics of a two-memristor based map is discovered. • The map exhibits diverse features. • Hardware implementation is presented. [ABSTRACT FROM AUTHOR]

In the last decade, researchers, who work in the field of nonlinear circuits, have the "dream" to use a real memristor, which is the only nonlinear fundamental circuit element, in a new or other reported nonlinear circuit in literature, in order to experimentally investigate chaos. With this intention, for the first time, a well-known nonlinear circuit, in which its nonlinear element has been replaced with a commercially available memristor (KNOWM memristor), is presented in this work. Interesting phenomena concerning chaos theory, such as period-doubling route to chaos, coexisting attractors, one-scroll and double-scroll chaotic attractors are experimentally observed. [ABSTRACT FROM AUTHOR]

This paper proposes a new chaotic system with a specific attractor which is bounded in a sphere. The system is offered in the spherical coordinate. Dynamical properties of the system are investigated in this paper. The system shows multistability, and all of its attractors are inside or on the surface of the specific sphere. Bifurcation diagram of the system displays an inverse period-doubling route to chaos. Lyapunov exponents of the system are studied to show its chaotic attractors and predict its bifurcation points. [ABSTRACT FROM AUTHOR]

In nonlinear dynamics, there is a continuous exploration of introducing systems with evidence of chaotic behavior. The presence of nonlinearity within system equations is crucial, as it allows for the emergence of chaotic dynamics. Given that quadratic terms represent the simplest form of nonlinearity, our study focuses on introducing a novel chaotic system characterized by only quadratic nonlinearities. We conducted an extensive analysis of this system's dynamical properties, encompassing the examination of equilibrium stability, bifurcation phenomena, Lyapunov analysis, and the system's basin of attraction. Our investigations revealed the presence of eight unstable equilibria, the coexistence of symmetrical strange repeller(s), and the potential for multistability in the system. [ABSTRACT FROM AUTHOR]

The effect of magnetic radiation is essential to be studied due to its favorable or unfavorable influences especially when it comes to biological systems. In this study, some effects of an external time-varying magnetic induction on the formation of spatiotemporal patterns in a model of excitable tissue are investigated. We have designed a two-dimensional neuronal network, in which the local dynamics of the neurons are governed by the four-variable magnetic Hindmarsh–Rose (HR) neuronal model. Besides, each neuron is set to be in chaotic regime. We have examined some values of the bifurcation parameters, namely the frequency and the amplitude of the external magnetic radiation. The resulting evolutionary spatiotemporal patterns have showed that an extremely low frequency provides the tissue more opportunity to support propagation process, while low frequency confines the evolution of the wave fronts. Moreover, higher amplitude of the sinusoidal radiation caused the wave propagation be impeded by an inherent obstacle that could limit the ultimate radius of the propagated wave. The resulting collective response of the designed neuronal network is represented in snapshots and the time series of a sampled neuron are plotted, as well. [ABSTRACT FROM AUTHOR]

An editorial focuses on the recent advancements in fractional calculus and its applications in physical systems. It emphasizes the utility of fractional calculus in describing complex systems with nonlocal characteristics. The versatility of fractional calculus across various scientific disciplines, including physics, engineering, and biology, is highlighted.

In this paper, by modifying a known two-dimensional oscillator, we obtain an interesting new oscillator with coexisting limit cycles and point attractors. Then by changing this new system to its forced version and choosing a proper set of parameters, we introduce a chaotic system with some very interesting features. In this system, not only can we see the coexistence of different types of attractors, but also a fascinating phenomenon: some initial conditions can escape from the gravity of nearby attractors and travel far away before being trapped in an attractor beyond the usual access. [ABSTRACT FROM AUTHOR]

Chaotic systems with a curve of equilibria have attracted considerable interest in theoretical researches and engineering applications because they are categorized as systems with hidden attractors. In this paper, we introduce a new three-dimensional autonomous system with cubic equilibrium. Fundamental dynamical properties and complex dynamics of the system have been investigated. Of particular interest is the coexistence of chaotic attractors in the proposed system. Furthermore, we have designed and implemented an electronic circuit to verify the feasibility of such a system with cubic equilibrium. [ABSTRACT FROM AUTHOR]

There has been an increasing interest in discovering no-equilibrium chaotic systems recently. In this paper, a novel three dimensional fractional-order chaotic system, which has no equilibrium, is introduced. Dynamics of the system has been studied. It is interesting that the system can exhibit coexisting chaotic attractors for the order as low as 2.7. The adjustable feature of a variable is studied by introducing a single controlled constant. Circuit implementation of the system is proposed to show its feasibility. In addition, we have designed the controllers to investigate coexisting synchronization types of such a new fractional-order system. Numerical examples have verified the proposed synchronization schemes. [ABSTRACT FROM AUTHOR]

Although chaotic systems have been intensively studied since the 1960s, new systems with mysterious features are still of interest. A novel chaotic system including hyperbolic functions is proposed in this work. Especially, the system has an infinite number of equilibrium points. Dynamics of the system are investigated by using non-linear tools such as phase portrait, bifurcation diagram, and Lyapunov exponent. It is interesting that the system can display coexisting chaotic attractors. An electronic circuit for realising the chaotic system has been implemented. Experimental results show a good agreement with theoretical ones. [ABSTRACT FROM AUTHOR]

For the past 4 years, there has been a rapid rise in the study of chaotic systems with curves of equilibria which are categorized as systems with hidden attractors. There is still significant controversy surrounding the shapes of equilibrium points. This paper presents a new three-dimensional autonomous chaotic system with hyperbolic sine equilibrium. Fundamental dynamical properties and complex dynamics of the system have been discovered by using equilibrium analysis, phase portrait, Poincaré map, bifurcation diagram and Lyapunov spectrum. It is crucial to note that there are bistable hidden chaotic attractors in the introduced system. Furthermore, in order to show the feasibility of the new system with hyperbolic sine equilibrium, its electronic circuit has been implemented. [ABSTRACT FROM AUTHOR]

Chaotic systems without equilibrium points have been investigated and received significant attention recently. In this work, we propose a new three-dimensional fractional-order chaotic system without equilibrium. Dynamics of the fractional-order system are investigated and a circuit implementation of the system by using electronic components is presented. Interestingly, bistable chaotic attractors of such fractional system are discovered. In addition, we are able to control and synchronize the system by using active control and unidirectional coupling. [ABSTRACT FROM AUTHOR]

Recent evidence suggests that there exists chaos in a few no-equilibrium systems. A chaotic system without equilibrium is proposed and studied in this work. It is worth noting that due to the absence of equilibrium, such a system belongs to a class of systems with hidden attractor. Dynamics properties and the feasibility of the system are investigated by using numerical simulations and circuit implementation. Interestingly, this no-equilibrium system has one variable with the freedom of offset boosting. [ABSTRACT FROM AUTHOR]

A new chaotic system having variable equilibrium is introduced in this paper. The presence of an infinite number of equilibrium points, a stable equilibrium, and no-equilibrium is observed in the system. Interestingly, this system is classified as a rare system with hidden attractors from the view point of computation. Complex dynamical behavior and a circuital implementation of the new system have been investigated in our work. [ABSTRACT FROM AUTHOR]

Wang-Chen system with only one stable equilibrium as well as the coexistence of hidden attractors has attracted increasing interest due to its striking features. In this work, the effect of state feedback on Wang-Chen system is investigated by introducing a further state variable. It is worth noting that a new chaotic system without equilibrium is obtained. We believe that the system is an interesting example to illustrate the conversion of hidden attractors with one stable equilibrium to hidden attractors without equilibrium. [ABSTRACT FROM AUTHOR]

Although chaotic systems with hidden attractors have been discovered recently, there are few investigations about relationships among them. This brief work introduces a novel chaotic system with only one stable equilibrium that is constructed by adding a tiny perturbation into a known chaotic flow having hidden attractors with a line equilibrium. [ABSTRACT FROM AUTHOR]

Pure phases of cubic and spherical FeS 2 nanocrystals (NCs) with the mean size of 80 nm and 30 nm, respectively, were obtained using trioctylamine and oleylamine as the solvents to dissolve the sulfur source via a facile and efficient hot injection method. The pure phase formation and shape control were strongly dependent on the concentration of active sulfur source (H 2 S) that could be formed by the reaction between the elemental sulfur and a primary amine. The chemically active sulfur source could facilitate the formation of a pure FeS 2 phase from a FeS phase via a Fe 3 S 4 phase. In addition, the active sulfur concentration is believed to be the main factor to drive the orientation attachment to obtain different shapes of FeS 2 NCs. The obtained FeS 2 pyrite NCs with excellent phase purity and good optical properties are believed to have potential applications to various energy devices including low-cost photovoltaics. [ABSTRACT FROM AUTHOR]

For the past five years there has been much attention to systems with uncountable equilibria. This work introduces a new system with an infinite number of equilibrium points. It is worth noting that equilibrium points, which located on a heart-shaped curve, lead the presence of hidden attractors in the system. By using phase portraits, bifurcation diagram, maximal Lyapunov exponents, dynamics of the system have been investigated. Moreover, an electronic implementation is proposed to illustrate the feasibility of the theoretical system. [ABSTRACT FROM AUTHOR]

Chaotic systems with an infinite number of equilibrium points and chaotic ones without equilibrium have received a significant attention in the last years because they belong to a class of systems with “hidden attractor”. In this work, we introduce a three-dimensional chaotic system displaying both hidden attractors with infinite equilibria and hidden attractors without equilibrium. Surprisingly, when the system exhibits hidden attractors with infinite equilibria, it has a rounded square curve of equilibrium points. Dynamical properties of the new system are analyzed through equilibrium points, phase portraits, bifurcation diagram, and maximal Lyapunov exponents. Furthermore, circuit implementation of the system is presented showing another approach to study such system as well as its feasibility. [ABSTRACT FROM AUTHOR]

In this note, hidden attractors in chaotic maps are investigated. Although there are many new researches on hidden attractors in chaotic flows, no investigation has been done on hidden attractors in maps based on our knowledge. In addition, a new interesting chaotic map with a bifurcation diagram starting from any desired period and then continuing with period doubling is introduced in this paper. [ABSTRACT FROM AUTHOR]

The chaotic systems with hidden attractors, such as chaotic systems with a stable equilibrium, chaotic systems with infinite equilibria or chaotic systems with no equilibrium have been investigated recently. However, the relationships between them still need to be discovered. This work explains how to transform a system with one stable equilibrium into a new system with an infinite number of equilibrium points by using a memristive device. Furthermore, some other new systems with infinite equilibria are also constructed to illustrate the introduced methodology. [ABSTRACT FROM AUTHOR]

Numerous chaotic systems have been studied in order to understand the phenomena of chaos. This paper introduces a novel three-dimensional chaotic system with the presence of infinite equilibria, that located on a piecewise linear curve. From a computational point of view, such system belongs to a class of nonlinear system with hidden attractor. Dynamics properties of this system are studied by means of phase portraits, bifurcation diagram, Lyapunov exponents and Kaplan–Yorke fractional dimension. Furthermore, experimental results show the feasibility of the theoretical system. [ABSTRACT FROM AUTHOR]

The presence of hidden attractors in dynamical systems has received considerable attention recently both in theory and applications. A novel three-dimensional autonomous chaotic system with hidden attractors is introduced in this paper. It is exciting that this chaotic system can exhibit two different families of hidden attractors: hidden attractors with an infinite number of equilibrium points and hidden attractors without equilibrium. Dynamical behaviors of such system are discovered through mathematical analysis, numerical simulations and circuit implementation. [ABSTRACT FROM AUTHOR]

A three-dimensional autonomous chaotic system with a circular equilibrium is investigated in this paper. Some dynamical properties and behaviors of this system are described in terms of equilibria, eigenvalue structures, bifurcation diagrams, Lyapunov exponents, time series and phase portraits. For specific parameters, the system displays periodic and chaotic attractors. The physical existence of the chaotic behavior found in the proposed system is verified by using the Orcad-PSpice software and experimental verification. A good qualitative agreement is shown between the experimental results, PSpice and numerical simulations. Furthermore, the commensurate fractional-order version of the system with a circular equilibrium is numerically studied. It is found that chaos exists in this system with order less than three. By tuning the commensurate fractional order, the system with a circular equilibrium displays chaotic and periodic attractors, respectively. Finally, chaos synchronization of identical fractional-order chaotic systems with a circular equilibrium is achieved by using the unidirectional linear error feedback coupling. It is shown that the fractional-order chaotic system can achieve synchronization for appropriate coupling strength. [ABSTRACT FROM AUTHOR]

Although many chaotic systems have been introduced in the literature, a few of them possess uncountably infinite equilibrium points. The aim of our short work is to widen the current knowledge of the chaotic systems with an infinite number of equilibria. A three-dimensional system with special properties, for example, exhibiting chaotic attractor with circular equilibrium, chaotic attractor with ellipse equilibrium, chaotic attractor with square-shaped equilibrium, and chaotic attractor with rectangle-shaped equilibrium, is proposed. [ABSTRACT FROM AUTHOR]

Discovering dynamical systems with hidden attractors has become an attractive topic recently. A novel four-dimensional continuous-time autonomous system with a cubic nonlinear term is introduced in this work. It is worth noting that this no-equilibrium system can generate hidden hyperchaotic attractors. The fundamental properties of such systems are investigated by means of equilibrium points, phase portrait, bifurcation diagram and Lyapunov exponents. In addition, an adaptive scheme has been presented to synchronize two such identical hyperchaotic systems. Moreover, an electronic circuit is also designed and implemented to verify the feasibility of the theoretical model. [ABSTRACT FROM AUTHOR]

Recently, many rare chaotic systems have been found including chaotic systems with no equilibria. However, it is surprising that such a system can exhibit multiscroll chaotic sea. In this paper, a novel no-equilibrium system with multiscroll hidden chaotic sea is introduced. Besides having multiscroll chaotic sea, this system has two more interesting properties. Firstly, it is conservative (which is a rare feature in three-dimensional chaotic flows) but not Hamiltonian. Secondly, it has a coexisting set of nested tori. There is a hidden torus which coexists with the chaotic sea. This new system is investigated through numerical simulations such as phase portraits, Lyapunov exponents, Poincaré map, and frequency spectra. Furthermore, the feasibility of such a system is verified through circuital implementation. [ABSTRACT FROM AUTHOR]

In this letter we investigate the role of complex fixed-points in finding hidden attractors in chaotic flows with no equilibria. If these attractors could be found by starting the trajectory in the neighborhood of complex fixed-points, maybe it would be better not to call them hidden. [ABSTRACT FROM AUTHOR]

A novel four-dimensional continuous-time autonomous hyperchaotic system which has no equilibrium is proposed in this paper. By starting from a third-order chaotic system and introducing a further variable performing state feedback, a four-dimensional system exhibiting hyperchaos is obtained. The basic dynamical properties of this system are investigated, such as equilibria and stability, Lyapunov exponent spectrum, and bifurcation diagrams. Furthermore, synchronization via diffusive coupling or control has been addressed. In the latter, parameter identification and synchronization are performed simultaneously. The circuit realization and experimental results are also presented. [ABSTRACT FROM AUTHOR]

This paper introduces a new no-equilibrium chaotic system that is constructed by adding a tiny perturbation to a simple chaotic flow having a line equilibrium. The dynamics of the proposed system are investigated through Lyapunov exponents, bifurcation diagram, Poincaré map and period-doubling route to chaos. A circuit realization is also represented. Moreover, two other new chaotic systems without equilibria are also proposed by applying the presented methodology. [ABSTRACT FROM AUTHOR]

Memristive systems have appeared in various application fields from nonvolatile memory devices and biological structures to chaotic circuits. In this paper, we propose two nonlinear circuits based on memristive systems in the presence of delay, i.e. memristive systems in which the state of the memristor depends on the time-delay. Both systems can exhibit chaotic behavior and, notably, in the second model, only a capacitor and a memristor are required to obtain chaos. [ABSTRACT FROM AUTHOR]

Memristor has received a significant amount of attention after a solid state implementation of it was realized in the Hewlett-Packard laboratories, because of the potential applications of such device in different areas. In this brief paper, we introduce a Cellular Neural/Nonlinear Network based on memristive cells for autowave generation. The basic cell consists of a three-component circuit (the parallel of a capacitor, an inductor and an active memristor) and displays slow-fast dynamics. Such a circuit is then connected through passive resistors to other identical cells to form a reaction-diffusion system. Simulation results show that the system is able to generate autowaves and open the way to the study of other complex phenomena like spiral waves or pattern formation in memristive circuits. [ABSTRACT FROM AUTHOR]

A novel memristive oscillator with infinite equilibria is proposed in this paper. The oscillator has six lines of equilibria, which make it different from known ones. Interestingly, the oscillator displays chaos and attractive features. Implementation of the oscillator via analog components is presented to verify its feasibility. [ABSTRACT FROM AUTHOR]

The classification of time series using machine learning (ML) analysis and entropy-based features is an urgent task for the study of nonlinear signals in the fields of finance, biology and medicine, including EEG analysis and Brain–Computer Interfacing. As several entropy measures exist, the problem is assessing the effectiveness of entropies used as features for the ML classification of nonlinear dynamics of time series. We propose a method, called global efficiency (GEFMCC), for assessing the effectiveness of entropy features using several chaotic mappings. GEFMCC is a fitness function for optimizing the type and parameters of entropies for time series classification problems. We analyze fuzzy entropy (FuzzyEn) and neural network entropy (NNetEn) for four discrete mappings, the logistic map, the sine map, the Planck map, and the two-memristor-based map, with a base length time series of 300 elements. FuzzyEn has greater GEFMCC in the classification task compared to NNetEn. However, NNetEn classification efficiency is higher than FuzzyEn for some local areas of the time series dynamics. The results of using horizontal visibility graphs (HVG) instead of the raw time series demonstrate the GEFMCC decrease after HVG time series transformation. However, the GEFMCC increases after applying the HVG for some local areas of time series dynamics. The scientific community can use the results to explore the efficiency of the entropy-based classification of time series in "The Entropy Universe". An implementation of the algorithms in Python is presented. [ABSTRACT FROM AUTHOR]

Landslides lead to widespread devastation and significant loss of life in mountainous regions around the world. Susceptibility assessments can provide critical data to help decision‐makers, for example, local authorities and other organizations, mitigating the landslide risk, although the accuracy of existing studies needs to be improved. This study aims to assess landslide susceptibility in the Thua Thien Hue province of Vietnam using deep neural networks (DNNs) and swarm‐based optimization algorithms, namely Adam, stochastic gradient descent (SGD), Artificial Rabbits Optimization (ARO), Tuna Swarm Optimization (TSO), Sand Cat Swarm Optimization (SCSO), Honey Badger Algorithm (HBA), Marine Predators Algorithm (MPA) and Particle Swarm Optimization (PSO). The locations of 945 landslides occurring between 2012 and 2022, along with 14 conditioning factors, were used as input data to build the DNN and DNN‐hybrid models. The performance of the proposed models was evaluated using the statistical indices receiver operating characteristic curve, area under the curve (AUC), root mean square error, mean absolute error (MAE), R2 and accuracy. All proposed models had a high accuracy of prediction. The DNN‐MPA model had the highest AUC value (0.95), followed by DNN‐HBA (0.95), DNN‐ARO (0.95), DNN‐Adam (0.95), DNN‐SGD (0.95), DNN‐TSO (0.93), DNN‐PSO (0.9) and finally DNN‐SCSO (0.83). High‐precision models have identified that the majority of the western region of Thua Thien Hue province is very highly susceptible to landslides. Models like the aforementioned ones can support decision‐makers in updating large‐scale sustainable land‐use strategies. [ABSTRACT FROM AUTHOR]

Understanding extreme events attracts scientists due to substantial impacts. In this work, we study the emergence of extreme events in a fractional system derived from a Liénard-type oscillator. The effect of fractional-order derivative on the extreme events has been investigated for both commensurate and incommensurate fractional orders. Especially, such a system displays multistability and coexistence of multiple extreme events. [ABSTRACT FROM AUTHOR]

In this paper, we propose and study a two-layer network composed of a Petri net in the first layer and a ring of coupled Hindmarsh–Rose neurons in the second layer. Petri nets are appropriate platforms not only for describing sequential processes but also for modeling information circulation in complex systems. Networks of neurons, on the other hand, are commonly used to study synchronization and other forms of collective behavior. Thus, merging both frameworks into a single model promises fascinating new insights into neuronal collective behavior that is subject to changes in network connectivity. In our case, the Petri net in the first layer manages the existence of excitatory and inhibitory links among the neurons in the second layer, thereby making the chemical connections time-varying. We focus on the emergence of different types of collective behavior in the model, such as synchronization, chimeras, and solitary states, by considering different inhibitory and excitatory tokens in the Petri net. We find that the existence of only inhibitory or excitatory tokens disturbs the synchronization of electrically coupled neurons and leads toward chimera and solitary states. [ABSTRACT FROM AUTHOR]

The article presents the correction for a article titled "Recent advancement of fractional calculus and its applications in physical systems" published online on December 8, 2023.