In this work control theory is used to formalize hyperchaos synchronization as a nonlinear observer design issue. Following approach, new systematic tool synchronize class of hyperchaotic systems via scalar transmitted signal developed. The proposed technique has been applied two well-known systems.

This paper describes a new fractional predator–prey discrete system of the Leslie type. In addition, non-linear dynamics suggested model are examined within framework commensurate and non-commensurate orders, using different numerical techniques such as Lyapunov exponent, phase portraits, bifurcation diagrams. These behaviours imply that type has rich complex dynamical properties influenced by incommensurate orders. Moreover, sample entropy test is carried out to measure complexity validate...

The Ueda oscillator is one of the most popular and studied nonlinear oscillators. Whenever subjected to external periodic excitation, it exhibits a fascinating array behaviors, including chaos. This research introduces novel fractional discrete system based on Υ-th Caputo difference thoroughly investigates its chaotic dynamics via commensurate incommensurate orders. Applying numerical methods like maximum Lyapunov exponent spectra, bifurcation plots, phase plane. We demonstrate emergence...

This paper presents an approach for generating new hyperchaotic attractors in a ring of Chua's circuits. By taking closed chain three circuits and exploiting sine functions as nonlinearities, the proposed technique enables 3D-scroll to be generated. In particular, shows that dynamics can designed by modifying six parameters related circuit nonlinearities.

The aim of this paper is to propose a new secure communications approach, obtained by combining into one scheme chaotic modulation, recursive encryption and masking. objective achieved designing control laws synchronize two hyperchaotic Lorenz systems with encrypted states via backstepping technique. process relies on Unified system, driven the as well algorithm that exploits an n-fold composition invertible function. A novel theorem proved, which assures transmitted message recovered at...

Few papers have been published to date regarding the stability of neural networks described by fractional difference operators. This paper makes a contribution topic presenting variable-order discrete network model and proving its Ulam–Hyers stability. In particular, two novel theorems are illustrated, one existence solution for proposed other Finally, numerical simulations three-dimensional two-dimensional were carried out highlight effectiveness conceived theoretical approach.

During the broadcast of Coronavirus across globe, many mathematicians made several mathematical models. This was, course, in order to understand forecast and behavior this epidemic’s spread precisely. Nevertheless, due lack much information about it, application models has become difficult reality sometimes impossible, unlike simple SIR model. In work, a simple, novel fractional-order discrete model is proposed study COVID-19 epidemic. Such shown its ability adapt periodic change number...

Memristors offer a crucial element for constructing discrete maps that have garnered significant attention in complex dynamics and various potential applications. In this study, we integrated memristive sigmoidal function to propose innovative mapping techniques. Our research confirms the amalgamation of memristor functions represents promising approach creating both 2D 3D maps. Particularly noteworthy are chaotic featuring multiple memristors, as highlighted our findings. Specifically...

We explore an oscillator with nonlinear functions and equilibrium lines that displays chaos. The stability complexity of the have been analysed investigated. presence multiple sets it apart from previously reported oscillators. synchronization is considered as application for secure communications. An observer designed by considering a transmitted signal state, in other words, injecting linear function satisfying Lipschitz’s condition to proposed oscillator. Moreover, adaptive control new obtained.

In this paper a general methodology for designing chaotic and hyperchaotic cryptosystems is developed. The basic idea to make the decrypter nonlinear observer state of encrypter. Referring concept, some propositions are given which enable plaintext be retrieved if proper structural properties system hold. proposed tool proves powerful flexible, since wide class can designed by exploiting different circuits. advantages suggested approach illustrated in detail. particular, utilization...

This tutorial investigates bifurcation and chaos in the fractional-order Chen system from time-domain point of view. The objective is achieved using Adomian decomposition method, which allows solution fractional differential equations to be written closed form. By taking advantage capabilities given by paper illustrates two remarkable findings: (i) exists with order as low 0.24, represents smallest value ever reported literature for any chaotic studied so far; (ii) it feasible show...

In this tutorial the chaotic behavior of fractional-order Chua's circuit is investigated from time-domain point view. The objective achieved using Adomian decomposition method, which enables solution fractional differential equations to be found in closed form. By exploiting capabilities offered by paper presents two remarkable findings. first result that a novel bifurcation parameter identified, is, q derivative. second chaos exists with order = 1.05, lowest reported literature for such...

A challenging topic in nonlinear dynamics concerns the study of fractional-order systems without equilibrium points. In particular, no paper has been published to date regarding presence hyperchaos these systems. This aims bridge gap by introducing a new example hyperchaotic system The conducted analysis shows that exists proposed when its order is as low 3.84. Moreover, an interesting application synchronization considered provided.

Abstract In this paper, we propose three fractional chaotic maps based on the well known 3D Stefanski, Rössler, and Wang maps. The dynamics of proposed are investigated experimentally by means phase portraits, bifurcation diagrams, Lyapunov exponents. addition, control laws introduced for these convergence controlled states towards zero is guaranteed stability theory linear discrete systems. Furthermore, a combined synchronization scheme whereby Rössler map considered as drive system with...

Chaotic systems with no equilibrium are a very important topic in nonlinear dynamics. In this paper, new fractional order discrete-time system is proposed, and the complex dynamical behaviors of such discussed numerically by means bifurcation diagram, largest Lyapunov exponents, phase portrait, 0–1 test. addition, one-dimensional controller proposed. The asymptotic convergence proposed established stability theory linear systems. Next, synchronization control scheme for two different hidden...

Currently, surgeons in operating rooms are forced to focus their attention both on the patient’s body and flat low-quality surgical monitors, order get all information needed successfully complete surgeries. The way data displayed leads disturbances of surgeon’s visuals, which may affect his performances, besides fact that other members team do not have proper visual tools able aid him. idea underlying this paper is exploit mixed reality support during procedures. In particular, proposed...

Most of the papers published so far in literature have focused on theoretical phenomena underlying formation chaos, rather than investigation potential applications chaos to real world. This paper aims bridge gap between theory and by presenting a survey very recent chaos. In particular, manuscript covers last three years describing different as reported during 2018 2020, including matter related symmetry properties chaotic systems. The topics covered herein include communications,...

Fractional-order systems have proved to be accurate in describing the spread of COVID-19 pandemic by virtue their capability include memory effects into system dynamics. This manuscript presents a novel fractional discrete-time model that includes number vaccinated individuals as an additional state variable equations. The paper shows proposed compartment model, described difference equations, has two fixed points, i.e., disease-free point and epidemic point. A new theorem is proven which...