Evolutionary Geomorphology

Chaotic neural networks consisting of a great number of chaotic neurons are able to reproduce the rich dynamics observed in biological nervous systems. In recent years, the memristor has attracted much interest in the efficient implementation of artificial synapses and neurons. This work addresses adaptive synchronization of a class of memristor-based neural chaotic systems using a novel adaptive backstepping approach. A systematic design procedure is presented. Simulation results have demonstrated the effectiveness of the proposed adaptive synchronization method and its potential in practical application of memristive chaotic oscillators in secure communication.

Recently, Leonov and Kuznetsov introduced a new class of nonlinear dynamical systems, which is called systems with hidden attractors, in contrary to the well-known class of systems with self-excited attractors. In this class, dynamical systems with infinite number of equilibrium points, with stable equilibria, or without equilibrium are classified. Since then, the study of chaotic systems with hidden attractors has become an attractive research topic because this new class of dynamical systems could play an important role not only in theoretical problems but also in engineering applications. In this direction, the proposed chapter presents the bidirectional and unidirectional coupling schemes between two identical dynamical chaotic systems with no-equilibrium points. As it is observed, when the value of the coupling coefficient is increased in both coupling schemes, the coupled systems undergo a transition from desynchronization mode to complete synchronization. Also, the simulation results reveal the richness of the coupled system’s dynamical behavior, especially in the bidirectional case, showing interesting nonlinear dynamics, with a transition between periodic, quasiperiodic and chaotic behavior as the coupling coefficient increases, as well as synchronization phenomena, such as complete and anti-phase synchronization. Various tools of nonlinear theory for the study of the proposed coupling method, such as bifurcation diagrams, phase portraits and Lyapunov exponents have been used.

To explore the impact of unknown terms and parameters on chaotic characteristics in chaotic systems, this paper examines the effects of state variables and unknown parameters. The study focuses on different combinations of linear, nonlinear, and constant terms It primarily investigates the role of multi-order state variables and their application to chaotic system models of varying dimensions. Firstly, by simulating a three-dimensional chaotic system, the paper analyzes how different combinations of nonlinear terms and initial conditions affect the system's chaotic behavior. Secondly, it evaluates the chaotic characteristics of a four-dimensional system, combining nonlinear terms with unknown parameters, using tools such as Lyapunov index diagrams, sample entropy, and dynamic trajectory plots. Finally, the paper integrates the constructed chaotic system with chaotic mapping to develop a two-level key chaotic image encryption system, thoroughly assessing its security and resistance to interference.

In recent years, a chaotic system is considered as an important pseudo-random source to pseudo-random number generators (PRNGs). This paper proposes a PRNG based on a modified logistic chaotic system. This chaotic system with fixed system parameters is convergent and its chaotic behavior is analyzed and proved. In order to improve the complexity and randomness of modified PRNGs, the chaotic system parameter denoted by floating point numbers generated by the chaotic system is confused and rearranged to increase its key space and reduce the possibility of an exhaustive attack. It is hard to speculate on the pseudo-random number by chaotic behavior because there is no statistical characteristics and infer the pseudo-random number generated by chaotic behavior. The system parameters of the next chaotic system are related to the chaotic values generated by the previous ones, which makes the PRNG generate enough results. By confusing and rearranging the output sequence, the system parameters of the previous time cannot be gotten from the next time which ensures the security. The analysis shows that the pseudo-random sequence generated by this method has perfect randomness, cryptographic properties and can pass the statistical tests.

A number of artificial neural models have been presented in the literature in an effort to suggest a more accurate representation of a single biological neuron. There are numerous publications on synthetic neurons that attempted to replicate a single biological neuron, however, such models were unable to generate the spiking patterns of a real biological neuron. Therefore, there is still scope to design and research improved spiking neural models that more accurately reflect the functions of a biological neuron. This motivation drives extensive modification of an artificial neuron model to produce the spike patterns of a real biological neuron. The modified single artificial neuron model that has been proposed exhibits the functions of a biological neuron. It’s still crucial to model spiking bio-neuron behavior. Modeling a spiking bio-neuron is still an important exercise in view of possible applications of the underlying features in the areas of neuromorphic engineering, cognitive radio, and spiking neural networks

Rather than the synchronization between identical chaotic systems, the "phase synchronization" among two or many nonlinear systems with distinct nonlinear parameters is investigated. It is observed that the dynamics of globally coupled ${N}_{1}$ periodic and ${N}_{2}$ chaotic systems can be reduced to that between matrix-coupled chaotic and periodic systems as the result of a two-step realization of the synchronization among the former systems. The same situation holds even for the array of distinct systems with a nearest-neighbor interaction.

ABSTRACTThis paper investigates the detection and control of chaotic behavior in field‐oriented control (FOC) systems for Permanent Magnet Synchronous Motors (PMSMs). Chaos, characterized by unpredictable and highly sensitive dynamics, can significantly impact the stability and performance of electrical machines. We begin by employing conventional methods, such as computing the Largest Lyapunov Exponent (LLE) and analyzing attraction basins, to distinguish between chaotic and periodic behaviors. Building on this foundation, we introduce a three‐stage neural network (NN)‐based control design for chaos synchronization, leveraging unsupervised learning (UL) to exploit the hidden properties of chaotic systems without explicit supervision. By integrating clustering, dimensionality reduction, and unsupervised modeling techniques, we demonstrate the potential to efficiently synchronize chaotic behavior in PMSMs. This approach not only enhances the understanding of chaotic dynamics but also enables the design of a robust NN‐based control strategy. The proposed methodology highlights the synergy between artificial intelligence (AI) and chaos theory, offering powerful tools for analyzing and controlling chaotic systems. Our findings pave the way for robust applications in complex industrial environments, where chaos synchronization can improve the reliability and efficiency of electrical machines. This study underscores the transformative potential of AI‐driven techniques and the three‐stage neural control framework in advancing the control of chaotic systems and their practical implementation in real‐world scenarios.

Nowadays, the quick detection of antibiotic resistance bacteria causes a major problem in the field of the development of new antibiotics against the resistant bacteria. To overcome this problem, genome editing tools like clustered regularly interspaced short palindromic repeats (CRISPR) can be used. The CRISPR-CAS system is useful for targeting and killing antibiotic-resistant bacteria by cleaving resistance genes. It is also used to detect antibioticresistant bacteria. CRISPR is made up of a single guide RNA and the CAS 9 protein. The single guide RNA is used to guide toward the target sequence, and the CAS 9 protein is an enzyme that cuts DNA and is used in conjunction with the guide RNA. This modified sgRNA contains a complementary sequence to that of the target resistance gene and recognizes the target resistance sequence; therefore, it is cleaved by CAS-9 protein, and the removal of the resistance gene turns bacteria into antibiotic-sensitive ones. One of the delivery systems of CRISPR into bacteria is via bacteriophage.

We demonstrate for the first time that spiral wave chimeras-spiral waves with spatially extended unsynchronzied cores-can exist in complex oscillatory and even locally chaotic homogeneous systems under nonlocal coupling. Using ideas from phase synchronization, we show in particular that the unsynchronized cores exhibit a distribution of different frequencies, thus generalizing the main concept of chimera states beyond simple oscillatory systems. In contrast to simple oscillatory systems, we find that spiral wave chimeras in complex oscillatory and locally chaotic systems are characterized by the presence of synchronization defect lines (SDLs), along which the dynamics follows a periodic behavior different from that of the bulk. Whereas this is similar to the case of local coupling, the type of the prevailing SDLs is very different.

Chaotic systems are widely used in various aspects such as information security, signal processing, and synchronous control. The structural complexity and the chaotic behavior of chaotic systems are two significant factors affecting their practical applications. In this paper, we propose a universal two-dimensional (2D) absolute-cosine chaotic model (ACCM). The 2D-ACCM is composed of a nonlinear bounded cosine function and an absolute value function. It can construct new chaotic maps with simple structures and complex chaotic behaviors on the basis of existing chaotic systems. To verify the effectiveness of the proposed system, we first choose two existing one-dimensional (1D) chaotic maps and one existing 2D chaotic map as the seed maps of the 2D-ACCM to generate two new maps, respectively. The results of chaotic behavior analysis show that these two new maps have more complex chaotic behavior and wider chaotic ranges than seed maps and some advanced chaotic maps. Then a hardware experiment platform based on a field-programmable gate array (FPGA) is used for the hardware implementation of the new maps. Finally, a simple chaos-based pseudo-random number generator (PRNG) is introduced to show the practical application. The experimental results show that the new maps can be easily implemented on the FPGA and the chaos-PRNGs can generate pseudo-random numbers with excellent randomness.

Electrical activity and synchronization of memristor synapse-coupled HR network based on energy method

Chaos theory deals with nonlinear things that are effectively impossible to predict or control, like turbulence, weather, the stock market, our brain states, and so on. These phenomena are often described by fractal mathematics, which captures the infinite complexity of nature. Rotated spin systems like stars, rotating solids, electromagnetic particles etc. are very interesting because they can in some circumstances exhibit chaotic precession. In this paper the chaotic system with “spin reversion” is described. The spin reversion means that direction of the rotation is reversed. The spin reversion is similar of phase modulation. The chaotic system can be “modulated” by different type of signal, e.g. sine wave, rectangle wave etc. The behavior of chaotic system with spin reversion was simulated and results of simulations are presented. This system can be used in different applications where chaotic behavior is important.

The existence of rotatory, oscillatory, and oscillatory-rotatory synchronization of two coupled chaotic phase systems is demonstrated in the paper. We find four types of transition to phase synchronization depending on coherence properties of motions, characterized by phase variable diffusion. When diffusion is small the onset of phase synchronization is accompanied by a change in the Lyapunov spectrum; one of the zero Lyapunov exponents becomes negative shortly before this onset. If the diffusion of the phase variable is strong then phase synchronization and generalized synchronization, occur simultaneously, i.e., one of the positive Lyapunov exponents becomes negative, or generalized synchronization even sets in before phase synchronization. For intermediate diffusion the phase synchronization appears via interior crisis of the hyperchaotic set. Soft and hard transitions to phase synchronization are discussed.

Fractional-order memristor-based chaotic jerk system with no equilibrium point and its fractional-order backstepping control

Phase synchronization may emerge from mutually interacting non-linear oscillators, even under weak coupling, when phase differences are bounded, while amplitudes remain uncorrelated. However, the detection of this phenomenon can be a challenging problem to tackle. In this work, we apply the Discrete Complex Wavelet Approach (DCWA) for phase assignment, considering signals from coupled chaotic systems and experimental data. The DCWA is based on the Dual-Tree Complex Wavelet Transform (DT-CWT), which is a discrete transformation. Due to its multi-scale properties in the context of phase characterization, it is possible to obtain very good results from scalar time series, even with non-phase-coherent chaotic systems without state space reconstruction or pre-processing. The method correctly predicts the phase synchronization for a chemical experiment with three locally coupled, non-phase-coherent chaotic processes. The impact of different time-scales is demonstrated on the synchronization process that outlines the advantages of DCWA for analysis of experimental data.