Hayder Natiq

Chaos is a significant concept in nonlinear dynamics, featuring numerous real-world examples and diverse applications, including cryptography. This study presents a novel chaotic system with a single fully unstable equilibrium point, where the equilibrium point is unstable in all directions — a property that is rare in chaotic systems, where the unstable equilibrium is typically a saddle. The dynamical properties of the proposed system are comprehensively analyzed through stability analysis, forward and backward bifurcation diagrams, Lyapunov exponent diagrams, and basin of attraction studies. Our analyses reveal that when the system’s equilibrium point is completely unstable, it generates monostable and multistable self-excited solutions, encompassing periodic and chaotic attractors. Conversely, in scenarios where the equilibrium point is stable, the system demonstrates periodic orbits, qualifying as hidden attractors. In the subsequent phase, we propose a sequential image encryption algorithm tailored for encrypting RGB images, utilizing the novel chaotic system as its foundation. The algorithm is rigorously evaluated using three prominent benchmark RGB images and subjected to various analyses and metric calculations, assuring its resilience against differential, statistical, and brute-force attacks.

In recent years, the study of neuronal models has provided significant insights into brain dynamics and neurological disorders. Map-based neuronal models, such as the Rulkov map, have gained considerable popularity due to their computational efficiency and ability to replicate complex neuronal dynamics. We thus here study the collective dynamics of an unidirectional ring network composed of three memristive Rulkov maps, with particular emphasis on synchronization patterns and their dependence on coupling types. By employing electrical and memristive/field couplings, we analyze the emergence of complete synchronization, lag synchronization, and phase synchronization under varying coupling strengths. Our findings highlight how diffusive-based synaptic pathways modulate synchronization and collective behavior in the network. The presented results also offer new perspectives on the role of coupling functions in shaping neuronal synchronization, and they reveal their deeper implications for understanding pathological brain states and for designing neuromorphic systems.

This work proposes a new two-dimensional dynamical system with complete nonlinearity. This system inherits its nonlinearity from trigonometric and hyperbolic functions like sine, cosine, and hyperbolic sine functions. This system gives birth to infinite but countable coexisting attractors before and after being forced. These two megastable systems differ in the coexisting attractors’ type. Only limit cycles are possible in the autonomous version, but torus and chaotic attractors can emerge after transforming to the nonautonomous version. Because of the position of equilibrium points in different attractors’ attraction basins, this system can simultaneously exhibit self-excited and hidden coexisting attractors. This system’s dynamic behaviors are studied using state space, bifurcation diagram, Lyapunov exponents (LEs) spectrum, and attraction basins. Finally, the forcing term’s amplitude and frequency are unknown parameters that need to be found. The sparrow search algorithm (SSA) is used to estimate these parameters, and the cost function is designed based on the proposed system’s return map. The simulation results show this algorithm’s effectiveness in identifying and estimating parameters of the novel megastable chaotic system.

The synchronization of higher-order networks presents a fascinating area of exploration within nonlinear dynamics and complex networks. Simultaneously, growing research interest focuses on uncovering synchronization dynamics in time-varying networks with time-dependent coupling structures, reflecting their prevalence in real-world systems like neuronal networks. Motivated by this, the present study delves into the synchronization phenomenon within a higher-order network incorporating a blinking coupling scheme. Blinking coupling is an on–off switching coupling that has been demonstrated to enhance synchronization effectively. Its efficacy stems from ensuring synchronization, as the master stability function (MSF) follows a linear pattern. In this study, our objective is to investigate such a time-varying coupling scheme in a higher-order network configuration. We investigate the influence of coupling parameters and blinking frequency on synchronization behavior. Notably, our findings demonstrate that as the blinking frequency increases, the network exhibits a gradual convergence toward the behavior of the average network. Furthermore, leveraging the analytical framework of MSF and the average synchronization error, we provide analytical and numerical evidence confirming that the MSF pattern within the average network transforms into a linear function. The synchronous and asynchronous regions also exhibit a clear separation demarcated by a linear curve across the coupling parameter space. Moreover, our results suggest that incorporating higher-order interactions fosters enhanced synchrony by effectively scaling the synchronization patterns to lower coupling parameter values.

This contribution introduces and investigates a small network of type-I, type-II, and type-III neurons. The considered network is made up of one Hindmarsh-Rose neuron (type-I), one FitzHugh-Nagumo neuron (type-II), and one Wilson neuron (type-III), all connected via a gap junction. The investigation of the stability in the presence of an external current revealed that the network is equilibrium-free; therefore, the network exhibits hidden collective behavior. The dynamical behavior of the model has been evaluated using the two-dimensional Largest Lyapunov Exponent (2D LLE), and it has been discovered that the network exhibits either regular or irregular firing patterns as the synaptic weights vary. It is also found that the network is able to exhibit the coexistence of firing activities involving coherent and incoherent spiking or coherent and incoherent bursting. Finally, the microcontroller integration of the set of considered neurons is presented, and the findings support those of the numerical simulations.

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.

Application of chaos in modeling natural phenomena and encryption encourages researchers to design new chaotic systems with exciting features. Here a chaotic jerk oscillator with different properties is proposed. Previous studies mainly used non-polynomial and piecewise linear terms to design the attractors’ shape. In the paper, the heart-shaped attractor is designed using just polynomial terms. This system is studied by considering its bifurcation diagram, Lyapunov exponent, and basin of attraction. These tools show that the proposed system has chaotic and periodic attractors that coexist in some parameter intervals. The oscillator does not have an equilibrium and has a heart-shaped attractor. Moreover, the connecting curves of the oscillator are considered to explore other structural properties. Numerical results confirm the analytical solutions for the system’s connecting curves. The interesting dynamics of the oscillator are used in an encryption and compression application.

Chaotic behavior can be observed in continuous and discrete-time systems. This behavior can appear in one-dimensional nonlinear maps; however, having at least three state variables in flows is necessary. Due to the lower mathematical complexity and computational cost of maps, lots of research has been conducted based on them. This paper aims to present a novel one-dimensional trigonometric chaotic map that is multi-stable and can act attractively. The proposed chaotic map is first analyzed using a single sinusoidal function; then, its abilities are expanded to a map with a combination of two sinusoidal functions. The stability conditions of both maps are investigated, and their different behaviors are validated through time series, state space, and cobweb diagrams. Eventually, the influence of parameter variations on the maps’ outputs is examined by one-dimensional and two-dimensional bifurcation diagrams and Lyapunov exponent spectra. Besides, the diversity of outputs with varying initial conditions reveals this map’s multi-stability. The newly designed chaotic map can be employed in encryption applications.

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.