Theory and applications of new fractional-order chaotic system under Caputo operator

This paper introduces the properties of a fractional-order chaotic system described by the Caputo derivative. The impact of the fractional-order derivative has been focused on. The phase portraits in different orders are obtained with the aids of the proposed numerical discretization, including the discretization of the Riemann-Liouville fractional integral. The stability analysis has been used to help us to delimit the chaotic region. In other words, the region where the order of the Caputo derivative involves and where the presented system in this paper is chaotic. The nature of the chaos has been established using the Lyapunov exponents in the fractional context. The schematic circuit of the proposed fractional-order chaotic system has been presented and simulated in via Mutltisim. The results obtained via Multisim simulation of the chaotic circuit are in good agreement with the results with Matlab simulations. That provided the fractional operators can be applied in real- worlds applications as modeling electrical circuits. The presence of coexisting attractors for particular values of the parameters of the presented fractional-order chaotic model has been studied.

Low-order modelling of the wake dynamics of an Ahmed body

We investigate the large-scale signature of the random switches between two mirrored turbulent wake states of flat-backed bodies. A direct numerical simulation (DNS) of the flow around an Ahmed body at a Reynolds number ( $Re$ ) of 10 000 is considered. Using proper orthogonal decomposition (POD), we identify the most energetic modes of the velocity field and build a low-dimensional model based on the first six fluctuating velocity modes capturing the characteristics of the flow dynamics during and between switches. In the absence of noise, the model produces random switches with characteristic time scales in agreement with the simulation and experiments. This chaotic model suggests that random switches are triggered by the increase of the vortex shedding activity. However, the addition of noise results in a better agreement in the temporal spectra of the coefficients between the model and the simulation.

Numerical solution of a fractal-fractional order chaotic circuit system

The dynamical system has an important research area and due to its wide applications many researchers and scientists working to develop new model and techniques for their solution. We present in this work the dynamics of a chaotic model in the presence of newly introduced fractal-fractional operators. The model is formulated initially in ordinary differential equations and then we utilize the fractal-fractional (FF) in power law, exponential and Mittag-Leffler to generalize the model. For each fractal-fractional order model, we briefly study its numerical solution via the numerical algorithm. We present some graphical results with arbitrary order of fractal and fractional orders, and present that these operators provide different chaotic attractors for different fractal and fractional order values. The graphical results demonstrate the effectiveness of the fractal-fractional operators.

Proposing and Dynamical Analysis of a Hyperjerk Piecewise Linear Chaotic System with Offset Boostable Variable and Hidden Attractors

Designing chaotic systems with different properties helps to increase our knowledge about real-world chaotic systems. In this article, a piecewise linear (PWL) term is employed to modify a simple chaotic system and obtain a new chaotic model. The proposed model does not have any equilibrium for different values of the control parameters. Therefore, its attractor is hidden. It is shown that the PWL term causes an offset boostable variable. This feature provides more flexibility and controllability in the designed system. Numerical analyses show that periodic and chaotic attractors coexist in some fixed values of the parameters, indicating multistability. Also, the feasibility of the system is approved by designing field programmable gate arrays (FPGA).

Compressed sensing based fingerprint imaging system using a chaotic model-based deterministic sensing matrix

A novel deterministic sensing matrix design approach applied to enable secured compressed sensing and transmission of fingerprint images. The performance of the sensing matrix was analyzed in detail by varying compressed sensing and security parameters. The number of sampling and sparse coefficient are the parameters taken under consideration from compressed sensing, whereas the encryption key is from the security scheme. The first stage in the performance study is acquiring the signal, and followed by sparsely modelling it using Orthogonal Matching Pursuit (OMP) algorithm. The sparse modelled data is multiplied by the proposed deterministic partial orthogonal Discrete Cosine Transform (DCT) sensing matrix to reduce its dimension and encrypt it. To introduce confusion on the DCT matrix rows, the pseudo-random permutation is applied to the DCT matrix rows before sensing matrix derivation. Additionally, recovering and decryption of the compressed image accomplished with the help of a convex optimization method. The results obtained from the simulation of the proposed system confirmed that a better Peak Signal to Noise Ratio (PSNR) than the recommended value for wireless transmission is archived using a sample below 25% without losing a significant number of fingerprint minutiae.

Compressed Sensing System for a Fingerprint Image Recognition Using Sensing Matrix with Chaotic Model-Based Deterministic Row Indexes

This paper proposes a novel design approach for a secured compressed sensing system for fingerprint sensing and transmission. In the proposed design, the first stage is acquiring the signal followed by sparsely modeling it using Orthogonal Matching Pursuit (OMP) algorithm then compressing. In addition to compressing, we multiply the sparse modeled data by a novel, deterministic, and partially orthogonal Discrete Cosine Transform (DCT) sensing matrix to guarantee its security. Furthermore, the construction of the sensing matrix uses a modified Multiplicative Linear Congruential Generator (MLCG) to select the row index appropriately from chaotically re-arranged rows of DCT pseudo-randomly. On the other hand, the compressed image's simultaneous recovery and decryption accomplished using a convex optimization method—the proposed system tested by employing different image and security assessment techniques. The results show that we have archived a better Peak Signal to Noise Ratio (PSNR) than the recommended value for wireless transmission using samples below 25%.

Compressed Sensing System for a Fingerprint Image Recognition Using Sensing Matrix with Chaotic Model-Based Deterministic Row Indexes

This paper proposes a novel design approach for a secured compressed sensing system for fingerprint imaging and its transmission. In the proposed design, the first stage is acquiring the signal followed by sparsely modeling it using Orthogonal Matching Pursuit (OMP) algorithm. In addition to compressing, to guaranty its security, we multiply the sparse modeled data by a novel deterministic partially orthogonal Discrete Cosine Transform (DCT) sensing matrix. Furthermore, the construction of the sensing matrix uses a modified Multiplicative Linear Congruential Generator (MLCG) to select the row index appropriately from chaotically re-arranged rows of DCT pseudo-randomly. On the other hand, the simultaneous recovering and decryption of the compressed image accomplished with the help of a convex optimization method. The proposed system tested by employing different image and security assessment techniques. The results show that we have archived better Peak Signal to Noise Ratio (PSNR) than the recommended value for wireless transmission using samples below 25%.