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We show that there is a residual subset $\mathcal{R}$ of ${\text{Diff}}^{\mathbf{1}}\mathbf{(}\mathit{M}\mathbf{)}$ such that for any $\mathit{f}\mathbf{\in }\mathcal{R}$ and any partially hyperbolic homoclinic class $\mathit{H}\mathbf{(}\mathit{p}\mathbf{,}\mathit{f}\mathbf{)}$ with one-dimensional central direction, the set of central Lyapunov exponents associated with the ergodic measure with ...

To address the limitations of existing chaotic maps, we proposed a non-degenerate n-dimensional (n ≥ 2) integer domain chaotic map (nD-IDCM) model that can construct any non-degenerate n-dimensional integer domain chaotic maps. Moreover, we ...

• A non-degenerate n-dimensional (n ≥ 2) integer domain chaotic map (nD-IDCM) model.
• Can construct any non-degenerate n-dimensional integer domain chaotic map.
• Maps constructed by nD-IDCM have desirable Lyapunov exponents.
• ...

This paper proposes a multiple-image encryption (MIE) approach that uses a novel exponent–sine–cosine (ESC) chaotic map along with the dynamic permutation and DNA-based diffusion. In the first phase of the proposed approach, the three components ...

Aside from humans, the instinct to run and hide from dangerous situations is ingrained in individuals of many other species. Taking refuge is a very common precautionary strategy among prey species to avoid direct contact with their predators. In ...

In this paper, we investigate the correlation between the Lyapunov exponent (LE) and the randomness in chaotic maps. The recently constructed chaotic map has certain limitations when used in cryptography. These limitations include the ...

• Aim to reveal the correlation between LE and randomness.
• Constructed a generic ...

Images are now often used as data carriers on the Internet, which has sped up the development of image encryption based on chaotic systems. The security of this image encryption algorithm is highly dependent on the stability of chaotic systems. This work ...

In this article, a new nonlinear four-dimensional hyperchaotic model is presented. The dynamical aspects of the complex system are analyzed covering equilibrium points, linear stability, dissipation, bifurcations, Lyapunov exponent, ...

The fact that very small changes cause unpredictable big changes in nature has led to the chaos theory. Many researchers focusing on chaos have improved this theory in several directions. One of the prominent areas in chaos theory is controlled ...

To overcome the limitations of classic fuzzy systems, including Type-1 and Type-2 fuzzy systems, and to propose a robust and flexible intelligent network, this paper presents a new fuzzy system called optimized cascade chaotic fuzzy system (OCCFS) ...

Assuming the uncertain parameter of a linear polytopic system to be uniformly distributed, we can prove that the system is almost sure exponentially stable if and only if its averaging system is stable. Computing the mathematical ...

The availability of the system is one of the main requirements of a multimedia-based e-health application that carries critical patient health information in the network environment. On the other hand, the Distributed Denial of Service (DDoS) ...

Many cryptographic schemes have been implemented, using the connection between chaos and cryptography. However, the present study introduces a new algorithm that, as a standard format, can be used in cyberspace. The substitution box (S-box) is one ...

One of the most popular techniques in the field of image retargeting or content-aware resizing a digital image is the seam-carving technique. The performance of image resizing algorithms based on seam-carving indicates that these algorithms are ...

Multichannel Electroencephalography-based Brain-Computer Interface (BCI) systems facilitate a communicating medium between the human brain and the outside world. BCI systems aim to translate human intentions into computer-based control commands by ...

In the present paper, we report the effect of nanoparticles in a three-species aquatic food chain model. It is assumed that due to the unavoidable interactions with nanoparticles, the growth rate of basal prey reduces. Fascinating ...

• We investigate the effect of nanoparticles in a three-species aquatic model.
• ...

In this paper, a novel combination of deep learning recurrent neural network and Lyapunov time is proposed to forecast the consumption of electricity load, in Greece, in normal/abrupt change value areas. Our method verifies the chaotic behavior of ...

The well-known Poincaré-Bendixson theorem tells us that the structure of the omega-limit sets of planar autonomous differential equations can be described by fixed points, limit cycles, or finite number of fixed points together with homoclinic and ...

At present times the topic of Chaos gain a lot of attention for the encryption/decryption methodology, yet we didn’t settled to get a good difference between conventional counterparts. Several chaotic maps can be considered sensitivity dependence ...

• DE and PSO algorithms are adapted for the optimization of both commensurate and incommensurate fractional-order chaotic oscillators.

The optimization of the Kaplan-Yorke dimension (D K Y) of fractional-order chaotic oscillators (FOCOs) is shown herein by applying two metaheuristics, namely: differential evolution and particle swarm optimization algorithms. The ...

Classical cryptosystems are not suitable for all situations for they fail to meet some current security requirements due to their small keyspace, which makes them prone to brute-force attacks, as well as their inefficiency in real-time ...