Master-slave synchronization of modified Wien bridge oscillators via adaptive current injection

In this paper, we propose a model of the water wheel under dry friction (the modi ed Lorenz-Malkus system). Dynamical features of this system are investigated and analyzed depending on the dry friction parameter. Particularly, we present the analysis of stationary points, Lyapunov exponents, bifurcation diagrams, and stochastic properties of the considered system. Based on the results of numerical simulations we showed that the dry friction may serve an effective mechanism to control the chaotic dynamics.

In this paper, a novel image encryption algorithm based on a new discrete chaotic system is presented. The chaotic characteristics of the new chaotic system are analyzed by phase diagram, Lyapunov exponent, bifurcation diagram and complexity analysis. The randomness of chaotic sequences is test by the NIST SP 800-22 test package. The calculation time with different length sequence is recorded. Based on the analyses results, a flexible encryption scheme is designed for 2D image and 3D image. The hash value which is calculated from the SHA-256 hash function is used to change the initial conditions of the discrete system firstly. And then, the chaotic sequences are used to scramble and spread the value for the images by Arnold matrix and DNA diffusion algorithm. The security analysis shows that the proposed encryption algorithm possesses higher security features to preserve the subject and resist conventional attack. The results of this paper offer a different realization scheme for protection of image files.

A new multi-scroll Chua’s circuit with composite hyperbolic tangent-cubic nonlinearity: Complex dynamics, Hardware implementation and Image encryption application

Simple Memristive Chaotic Systems with Complex Dynamics

A theoretical analysis of a SEAIJR model of Spanish flu with fractional derivative

Modeling the dynamics of anti-microbial resistant cholera infection with reinfection

Initial value-related dynamical analysis of the memristor-based system with reduced dimensions and its chaotic synchronization via adaptive sliding mode control method

In different areas like physics, engineering, biology, for example, to predict the behavior of composite systems one has to solve complex differential equations. This paper reviews the direct numerical method as a computational technique used to solve the difficult Equations above. Therefore, the application of this method will help us identify the behavior of large systems. Some of the methods used in the analysis include; creation of bifurcation diagrams to analyze how the system responds to different parameters, examine of Lyapunov exponent in an effort to understand the initial conditions' sensitiveness. Thus, in this paper uses the mentioned techniques to provide a clear understanding of the naturel of interactions within such systems. In addition to evidencing the value of direct numerical methods for rendering a precise portrayal of the systems, this study also improves our general comprehension of the underlying theory of such systems.

Novel multiple-image encryption algorithm based on a two-dimensional hyperchaotic modular model

Melnikov's criteria and chaos in systems with fractional order deflection

Rich dynamics of a discrete two dimensional predator–prey model using the NSFD scheme

Nonlinear vehicle dynamics are omnipresent and significantly affect driving performance and safety. Jumping vehicles, in particular, exhibit strong nonlinearities that can lead to severe vibrations and steering instabilities. This study investigates the dynamics of nonlinear jumping vehicle models with and without time delay to clarify their fundamental characteristics. Quarter- and half-car models with jumping nonlinearity are considered, and delayed feedback is introduced as an active suspension control. Numerical simulations under periodic and random excitations reveal several key findings as follows. Both models exhibit sudden, discontinuous transitions from periodic to chaotic dynamics in their bifurcation diagrams. A general relationship between the time period of periodic motions and the forcing period is also identified and further validated using a forced Duffing oscillator with time delay, confirming its generic nature. With the introduction of delay, both in-phase and out-of-phase motions emerge between the front and rear, even under simultaneous excitation. From a practical standpoint, in-phase motion is undesirable, making the realization of out-of-phase behavior within a specific delay range important for improving ride performance. This study identifies the stability regions of nonlinear quarter- and half-car models using bifurcation diagrams, Lyapunov exponents, and frequency response curves. In addition, the inclusion of a time delay is shown to effectively stabilize chaotic motions into periodic responses and to induce both in-phase and out-of-phase oscillations. These findings demonstrate that time delay plays a significant role in enhancing the stability of vehicle models with jumping nonlinearities.

Dynamical behavior, chaos control and synchronization of a memristor-based ADVP circuit

Vibrational resonance (VR) has been extensively studied in symmetric circuits, but research on this phenomenon in asymmetric electronic circuits is understudied. The current study aims to model a novel asymmetric electronic circuit and investigate the occurrence of VR in the circuit. This oscillator shows changes according to four control parameters, with the aid of two buffers. The amplification of signals in electronic circuits gives interesting results, vibrational resonance is one of the phenomena which is based on the amplification of signals. In this study, the asymmetric strength caused by the potentiometers and the frequencies influence are the major aims explored. Interestingly, the circuit shows different types of behaviors that are pointed out through waveform profiles, bifurcation diagrams, largest Lyapunov exponent, and the phase portraits. The dynamic of the system is studied theoretically, numerically and by Pspice Simulation. The Pspice estimates match with numerical simulations. We use the response Q(ω) method, based on the sine and cosine of the Fourier component to study VR. Our discovery suggests that the asymmetric parameter and the amplitude of the high frequency, both affect the occurrence of vibrational resonance.

A new fractional-order hyperchaotic memristor oscillator: Dynamic analysis, robust adaptive synchronization, and its application to voice encryption