Multistable ghost attractors in a switching laser system.

This paper studies the effects of a switching parameter on the dynamics of a multistable laser model. The laser model represents multistability in distinct ranges of parameters. We assume that the system's parameter switches periodically between different values. Since the system is multistable, the presence of a ghost attractor is also dependent on the initial condition. It is shown that when the composing subsystems are chaotic, a periodic ghost attractor can emerge and vice versa, depending on the initial conditions. In contrast to the previous studies in which the attractor of the fast blinking systems approximates the average attractor, here, the blinking attractor differs from the average in some cases. It is shown that when the switching parameter values are distant from their average, the blinking and the average attractors are different, and as they approach, the blinking attractor approaches the average attractor too.

The Intricacies of Sprott-B System with Fractional-Order Derivatives: Dynamical Analysis, Synchronization, and Circuit Implementation.

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.

An optimization-based algorithm for obtaining an optimal synchronizable network after link addition or reduction.

Achieving a network structure with optimal synchronization is essential in many applications. This paper proposes an optimization algorithm for constructing a network with optimal synchronization. The introduced algorithm is based on the eigenvalues of the connectivity matrix. The performance of the proposed algorithm is compared with random link addition and a method based on the eigenvector centrality. It is shown that the proposed algorithm has a better synchronization ability than the other methods and also the scale-free and small-world networks with the same number of nodes and links. The proposed algorithm can also be applied for link reduction while less disturbing its synchronization. The effectiveness of the algorithm is compared with four other link reduction methods. The results represent that the proposed algorithm is the most appropriate method for preserving synchronization.

Dynamic analysis of the discrete fractional-order Rulkov neuron map.

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.

Dynamics of a two-layer neuronal network with asymmetry in coupling.

Investigating the effect of changes in neuronal connectivity on the brain's behavior is of interest in neuroscience studies. Complex network theory is one of the most capable tools to study the effects of these changes on collective brain behavior. By using complex networks, the neural structure, function, and dynamics can be analyzed. In this context, various frameworks can be used to mimic neural networks, among which multi-layer networks are a proper one. Compared to single-layer models, multi-layer networks can provide a more realistic model of the brain due to their high complexity and dimensionality. This paper examines the effect of changes in asymmetry coupling on the behaviors of a multi-layer neuronal network. To this aim, a two-layer network is considered as a minimum model of left and right cerebral hemispheres communicated with the corpus callosum. The chaotic model of Hindmarsh-Rose is taken as the dynamics of the nodes. Only two neurons of each layer connect two layers of the network. In this model, it is assumed that the layers have different coupling strengths, so the effect of each coupling change on network behavior can be analyzed. As a result, the projection of the nodes is plotted for several coupling strengths to investigate how the asymmetry coupling influences the network behaviors. It is observed that although no coexisting attractor is present in the Hindmarsh-Rose model, an asymmetry in couplings causes the emergence of different attractors. The bifurcation diagrams of one node of each layer are presented to show the variation of the dynamics due to coupling changes. For further analysis, the network synchronization is investigated by computing intra-layer and inter-layer errors. Calculating these errors shows that the network can be synchronized only for large enough symmetric coupling.

Investigation of vaccination game approach in spreading covid-19 epidemic model with considering the birth and death rates.

In this study, an epidemic model for spreading COVID-19 is presented. This model considers the birth and death rates in the dynamics of spreading COVID-19. The birth and death rates are assumed to be the same, so the population remains constant. The dynamics of the model are explained in two phases. The first is the epidemic phase, which spreads during a season based on the proposed SIR/V model and reaches a stable state at the end of the season. The other one is the "vaccination campaign", which takes place between two seasons based on the rules of the vaccination game. In this stage, each individual in the population decides whether to be vaccinated or not. Investigating the dynamics of the studied model during a single epidemic season without consideration of the vaccination game shows waves in the model as experimental knowledge. In addition, the impact of the parameters is studied via the rules of the vaccination game using three update strategies. The result shows that the pandemic speeding can be changed by varying parameters such as efficiency and cost of vaccination, defense against contagious, and birth and death rates. The final epidemic size decreases when the vaccination coverage increases and the average social payoff is modified.

In search of COVID-19 transmission through an infected prey.

This paper considers a nonlinear dynamical model of an ecosystem, which has been established through combining the classical Lotka-Volterra model with the classic SIR model. This nonlinear system consists of a generalist predator that subsists on two prey species in which disease is becoming endemic in one of them. The dynamical analysis methods prove that the system has a chaotic attractor and extreme multistability behavior, where there are infinitely many attractors that coexist under certain conditions. The occurrence of extreme multistability demonstrates the high sensitivity of the system for the initial conditions, which means that tiny changes in the original prey species could enlarge and be widespread, and that could confirm through studying the complexity of the time series of the system's variables. Simulation results of the sample entropy algorithm show that the changes in the system's variables expand over time. It is reasonable now to consider the endemic in the prey species of the system could evolve to be pandemic such as COVID-19. Consequently, our results could provide a foresight about the unpredictability of the COVID-19 outbreak in its original host species as well as after the transmission to other species such as humans.

Enhancing Chaos Complexity of a Plasma Model through Power Input with Desirable Random Features.

The present work introduces an analysis framework to comprehend the dynamics of a 3D plasma model, which has been proposed to describe the pellet injection in tokamaks. The analysis of the system reveals the existence of a complex transition from transient chaos to steady periodic behavior. Additionally, without adding any kind of forcing term or controllers, we demonstrate that the system can be changed to become a multi-stable model by injecting more power input. In this regard, we observe that increasing the power input can fluctuate the numerical solution of the system from coexisting symmetric chaotic attractors to the coexistence of infinitely many quasi-periodic attractors. Besides that, complexity analyses based on Sample entropy are conducted, and they show that boosting power input spreads the trajectory to occupy a larger range in the phase space, thus enhancing the time series to be more complex and random. Therefore, our analysis could be important to further understand the dynamics of such models, and it can demonstrate the possibility of applying this system for generating pseudorandom sequences.

Can hyperchaotic maps with high complexity produce multistability?

In this paper, we investigate the dynamical behavior in an M-dimensional nonlinear hyperchaotic model (M-NHM), where the occurrence of multistability can be observed. Four types of coexisting attractors including single limit cycle, cluster of limit cycles, single hyperchaotic attractor, and cluster of hyperchaotic attractors can be found, which are unusual behaviors in discrete chaotic systems. Furthermore, the coexistence of asymmetric and symmetric properties can be distinguished for a given set of parameters. In the endeavor of chaotification, this work introduces a simple controller on the M-NHM, which can add one more loop in each iteration, to overcome the chaos degradation in the multistability regions.

Dynamics and Complexity of a New 4D Chaotic Laser System.

Derived from Lorenz-Haken equations, this paper presents a new 4D chaotic laser system with three equilibria and only two quadratic nonlinearities. Dynamics analysis, including stability of symmetric equilibria and the existence of coexisting multiple Hopf bifurcations on these equilibria, are investigated, and the complex coexisting behaviors of two and three attractors of stable point and chaotic are numerically revealed. Moreover, a conducted research on the complexity of the laser system reveals that the complexity of the system time series can locate and determine the parameters and initial values that show coexisting attractors. To investigate how much a chaotic system with multistability behavior is suitable for cryptographic applications, we generate a pseudo-random number generator (PRNG) based on the complexity results of the laser system. The randomness test results show that the generated PRNG from the multistability regions fail to pass most of the statistical tests.