Abstract In this article, asymmetrical novel system with two exponential functions, which can show hyperchaotic behavior, has been proposed. Although new possesses only one unstable equilibrium. The dynamical behaviors of such are discovered by computing the Lyapunov exponents and bifurcation diagram. Furthermore, synchronization proposed also presented an adaptive approach identical systems. An application to image encryption obtained.

It is well known that, compared to low-dimension chaotic systems, three-dimensional systems have a wider parameter range, more complicated behaviour, and better unpredictability. This fact motivated us introduce novel image encryption method that employs system. We proposed conservative system can exhibit behaviour involving hyperbolic functions. The dynamical behaviours of the are discovered by calculating Lyapunov exponents bifurcation diagrams. Thereafter, we designed an based on 4×4...

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.

The stability of differential equations is one the most important aspects to consider in dynamical system theory. Chaotic systems were classified according as multi-stable systems; with a single stable equilibrium; bi-stable and, recently, mega-stable systems. Mega-stability refers infinity countable nested attractors periodically forced non-autonomous system. Many researchers attempted present simple In this paper, we investigated mega-stability damped following different order cases:...

We present a hyperchaotic oscillator with two linear terms and seven nonlinear that displays special algebraic properties. Notably, the introduced features distinct equilibrium types: single-point, line, spherical equilibria. The exhibits attractive dynamics like hyperchaos wing attractors. To gain better understanding, we provide bifurcation Lyapunov exponents. Kolmogorov–Sinai entropy is applied to show complexity of oscillator. A microcontroller realization confirms reliability proposed...

For continuous functions $f$ with zero mean on the circle we consider Birkhoff sums $f(n,x,h)$ generated by rotations $2\pi h$, where $h$ is an irrational number. The main result asserts that growth rate of sequence $\max_x f(n,x,h)$ as $n \to \infty$ depends only uniform convergence to means $\frac{1}{n}f(n,x,h)$. Namely, show for any $\sigma_k 0$ and there exists a function such increases faster than $n\sigma_n$. We also not trigonometric polynomial exist which some subsequence f(n_k,x,h)$...

This paper proposes a system with an absolute term, exhibiting chaos. The system's dynamics are examined by computation of bifurcation and Lyapunov exponents. has countable finite coexisting nested attractors. features the make it suitable for secure applications. is combined 4×4 Toeplitz matrix to generate encryption algorithm, validated using security performance analysis. Combining proposed improves pixel distribution's randomness, significantly increasing security. test results showed...

Let G be a finite order graph. Its resolvent matrix and its energy are respectively given by Rξ(A(G)) = (A(G) – ξI)–1 ER(G) Σn i 1 (n λi)–1. For some classes of weighted graphs, we know that λ1 n which means the formula for is not applicable. In this work, pseudo-resolvent those graphs obtained where n.

In 2020, J. Sprott proposed a new three dimensional chaotic system with special features such like 1) dissipative and time-reversible; 2) no equilibrium point; 3) lien of initial conditions goes to the attractor. We observed that an extension so-called Sprott's 2020 four complex dynamics showed either or hyperchaotic unbounded orbits. this paper, novel five based on has been proposed. The shows hyperchaotic. can be classified as hidden attractor where point appeared self-excited unusual...

The complex dynamics of a newly proposed 4D hyperchaotic Lorenz-type system are studied in this paper. sufficient conditions for the emergence and stability periodic solutions at bifurcation points derived using averaging theory. ultimate boundedness is also established.

Let G be a simple graph of order N, the concept resol-vent energy G; i.e. ER(G)=sum_{i=1}^N (N - λi)^{-1} was established in Resolvent Energy Graphs, MATCH commun. Math. comput. chem., 75 (2016), 279-290. In this paper we study set resol-vents energies which it is called pseudospectrum PS(G). For large value resolvent ER(G) and real eigenvalues, establish number properties PS(G): complex some examples PS(G) are given.

В работе рассмотрены суммы Биркгофа $f(n,x,h)$ для непрерывных функций $f$ с нулевым средним на окружности, порожденные поворотами углы $2\pi h$, где число $h$ иррациональное. Основной результат утверждает, что единственным ограничением скорость роста последовательности $\max_x f(n,x,h) $ при $n \to \infty$ является равномерное стремление к нулю средних $\frac{1}{n}f(n,x,h)$. А именно показано, любой $\sigma_k 0$ и любого иррационального существует такая функция $f$, последовательность...

Abstract We study hypercyclicity of truncated Toeplitz operators in the model space H 2 (D) θ θH (Ө) where is inner function and Hardy space. In this paper, necessary condition operator given.

In this article, we study the resolvent energy and pseudospectrum of a sequence C12n fullerenes with exactly 12n carbon atoms. particular, these together their lower bounds are obtained.

Its well known that there are a limited number of method which associate group theory to graph theory. In this paper, we propose new and obtain novel kind graphs. Some important application like energy was established the proposed graph.