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1

Spike patterns and chaos in a map-based neuron model

Bartłomiejczyk Piotr, Llovera Trujillo Llovera, Signerska-Rynkowska Justyna

International Journal of Applied Mathematics and Computer Science

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2023

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Vol. 33, no. 3

395--408

EN

The work studies the well-known map-based model of neuronal dynamics introduced in 2007 by Courbage, Nekorkin and Vdovin, important due to various medical applications. We also review and extend some of the existing results concerning β-transformations and (expanding) Lorenz mappings. Then we apply them for deducing important properties of spike-trains generated by the CNV model and explain their implications for neuron behaviour. In particular, using recent theorems of rotation theory for Lorenz-like maps, we provide a classification of periodic spiking patterns in this model.

2

Probing 3D chaotic Thomas’ cyclically attractor with multimedia encryption and electronic circuitry

Khan NajeebAlam, Qureshi Muhammad Ali, Akbar Saeed, Ara Asmat

Archives of Control Sciences

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2023

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Vol. 33, No. 1

239--271

EN

This study investigates Thomas’ cyclically symmetric attractor dynamics with mathematical and electronic simulations using a proportional fractional derivative to comprehend the dynamics of a given chaotic system. The three-dimensional chaotic flow was examined in detail with Riemann-Liouville derivative for different values of the fractional index to highlight the sensitivity of chaotic systems with initial conditions. Thus, the dynamics of the fractional index system were investigated with Eigenvalues, Kaplan-Yorke dimension, Lyapunov exponent, and NIST testing, and their corresponding trajectories were visualized with phase portraits, 2D density plot, and Poincaré maps. After obtaining the results, we found that the integer index dynamics are more complex than the fractional index dynamics. Furthermore, the chaotic system circuit is simulated with operational amplifiers for different fractional indices to generate analog signals of the symmetric attractor, making it an important aspect of engineering. The qualitative application of our nonlinear chaotic system is then applied to encrypt different data types such as voice, image, and video, to ensure that the developed nonlinear chaotic system can widely applied in the field of cyber security.

3

Dynamical properties of a modified chaotic Colpitts oscillator with triangular wave non-linearity

Suresh Rasappan, Sathish Kumar Kumaravel, Regan Murugesan, Niranjan Kumar K. A., Narmada Devi R., Obaid Ahmed J.

Archives of Control Sciences

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2023

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Vol. 33, No. 1

25--53

EN

The purpose of this paper is to introduce a new chaotic oscillator. Although different chaotic systems have been formulated by earlier researchers, only a few chaotic systems exhibit chaotic behaviour. In this work, a new chaotic system with chaotic attractor is introduced for triangular wave non-linearity. It is worth noting that this striking phenomenon rarely occurs in respect of chaotic systems. The system proposed in this paper has been realized with numerical simulation. The results emanating from the numerical simulation indicate the feasibility of the proposed chaotic system. More over, chaos control, stability, diffusion and synchronization of such a system have been dealt with.

4

Bifurcation analysis, circuit design and sliding mode control of a new multistable chaotic population model with one prey and two predators

Vaidyanathan Sundarapandian, Benkouider Khaled, Sambas Aceng, Darwin P.

Archives of Control Sciences

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2023

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Vol. 33, No. 1

127--153

EN

In this work, we report a new chaotic population biology system with one prey and two predators. Our new chaotic population model is derived by introducing two nonlinear interaction terms between the prey and predator-2 to the Samardzija-Greller population biology system (1988). We show that the new chaotic population biology system has a greater value of Maximal Lyapunov Exponent (MLE) than the Maximal Lyapunov Exponent (MLE) of the Samardzija-Greller population biology system (1988). We carry out a detailed bifurcation analysis of the new chaotic population biology system with one prey and two predators. We also show that the new chaotic population biology model exhibits multistability with coexisting chaotic attractors. Next, we use the integral sliding mode control (ISMC) for the complete synchronization of the new chaotic population biology system with itself, taken as the master and slave chaotic population biology systems. Finally, for practical use of the new chaotic population biology system, we design an electronic circuit design using Multisim (Version 14.0).

5

A new modified WINDMI jerk system with exponential and sinusoidal nonlinearities, its bifurcation analysis, multistability, circuit simulation and synchronization design

Mohamed Mohamad Afendee, Vaidyanathan Sundarapandian, Hannachi Fareh, Sambas Aceng, Darwin P.

Archives of Control Sciences

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2023

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Vol. 33, No. 4

711--735

EN

In this work, a new 3-D modified WINDMI chaotic jerk system with exponential and sinusoidal nonlinearities is presented and its dynamical behaviours and properties are investigated. Firstly, some properties of the system are studied such as equilibrium points and their stability, Lyapunov exponents and Kaplan-Yorke dimension. Also, we study the new jerk system dynamics using numerical simulations and analyses, including phase portraits, Lyapunouv exponent spectrum, bifurcation diagram and Poincaré map, 0-1 test. Next, we exhibit that the new 3-D chaotic modified WINDMI jerk system has multistability with coexisting chaotic attractors. Moreover, we design an electronic circuit using MultiSim 14.1 for real implementation of the modified WINDMI chaotic jerk system. Finally, we design an active synchronization scheme for the complete synchronization of the modified WINDMI chaotic jerk systems via backstepping control.

6

Badania symulacyjne wpływu wybranych zakłóceń napięcia zasilania na prądy silnika indukcyjnego małej mocy

Hallmann Damian, Jankowski Piotr

Przegląd Elektrotechniczny

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2022

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R. 98, nr 11

195--200

PL

Stały wzrost mocy odbiorników nieliniowych w tym przekształtników powoduje pojawienie się w sieci zasilającej, zwłaszcza typu miękkiego (np. okrętowy system elektroenergetyczny), zaburzeń charakteryzujących się pojawieniem subharmonicznych i interharmonicznych. Artykuł prezentuje wyniki badań symulacyjnych wskazujących stopień wpływu zawartości tych zaburzeń w napięciu zasilania silnika indukcyjnego na prądy silnika. Wpływ powyższych zaburzeń badano dodatkowo z użyciem wskaźników zachowań chaotycznych. Do badań wykorzystano autorski model silnika indukcyjnego zrealizowany w środowisku ANSYS Electronics Desktop.

EN

The continuous increase in the power of non-linear receivers, including converters, causes the appearance in the supply network, especially of the soft type (e.g. the marine power system), disturbances characterized by the appearance of subharmonics and interharmonics. This article presents the results of simulation studies showing the degree of influence of the content of these disturbances in the supply voltage of an induction motor on its currents. The impact of the above mentioned disorders was additionally investigated with the use of indicators of chaotic behaviour. The original model of the induction motor, realized in the ANSYS Electronics Desktop environment, was used for the tests.

7

Control of optical chaos spectrum in semiconductor laser for secure RoF communication

Mazhar Danish Ali, Ali Syed Zafar, Islam Muhammad Khawar

Optica Applicata

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2022

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Vol. 52, nr 4

485--495

EN

A critical requirement in optical chaos based secure radio over fiber (RoF) system design is the ability to control center frequency, spectral bandwidth, power level and signature of chaos to submerge message with sufficient horizontal and vertical margins both in time and frequency domains. Once frequency domain masking is completely achieved, time domain masking is met automatically, the former being more stringent. In a direct modulated semiconductor laser, the three control parameters are bias current (Ibias), modulation current (Imod) and modulation frequency (ωa). It is found that Imod increases bandwidth and amplitude dynamic range of chaotic pulses. Ibias increases the cavity power and hence average peak amplitude of laser chaotic pulses. The modulation frequency increases the speed of overall cavity dynamics and hence is used to increase the bandwidth of chaos but a corresponding increase in bias and modulation currents is required to support high repetition pulses. The results show relationship between three control parameters (bias current, modulation current and modulation frequency) in a direct modulated semiconductor laser and optical chaos bandwidth using regression.

8

A new multistable jerk chaotic system, its bifurcation analysis, backstepping control-based synchronization design and circuit simulation

Vaidyanathan Sundarapandian, Benkouider Khaled, Sambas Aceng

Archives of Control Sciences

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2022

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Vol. 32, No. 1

123--152

EN

In this work, we present results for a new dissipative jerk chaotic system with three quadratic terms in its dynamics.We describe the bifurcation analysis for the new jerk system and also show that the proposed system exhibits multi-stability. Next, we describe a backstepping control-based synchronization design for a pair of new jerk chaotic systems. MATLAB simulations are put forth to exhibit the various findings in this work. Furthermore, we exhibit a circuit simulation for the new jerk system using MultiSim.

9

Nonlinear dynamics and multifractal analysis of minimum–maximum temperature and solar radiation over Lagos State, Nigeria

Akinsusi Joshua, Ogunjo Samuel, Fuwape Ibiyinka

Acta Geophysica

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2022

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Vol. 70, no 5

2171--2178

EN

This study focuses on investigating the chaotic and multifractal behavior of atmospheric time series of solar radiation (solar), maximum temperature (Tmax), and minimum temperature (Tmin) over Lagos State for a period of 24 years. Chaotic quantifiers such as sample entropy, Lyapunov exponent, and correlation dimension were employed to unveil the chaotic nature of the time series. Values of Lyapunov exponents obtained for the three parameters were in the range 0.251–0.261, which confirms chaos in the time series. The scaling properties of the time series were revealed by applying the Multifractal Detrended Fluctuation Analysis (MFDFA). Based on the multifractal strength, we infer that the dynamics of solar radiation (0.932) is different from that of maximum temperature (0.155) and minimum temperature (0.198). The time series have a long-range correlation and broad probability distribution. Results obtained showed that the time series is chaotic and exhibited a multifractal behavior. The results also show that chaotic and multifractal analyses are useful in unveiling the complex dynamics of the atmosphere.

10

Cryptanalysis of a Bilateral-Diffusion image encryption algorithm based on dynamical compound chaos

Alshammari Badr Mesned

Przegląd Elektrotechniczny

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2021

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R. 97, nr 1

128--131

EN

This paper proposes an attack on a recently proposed cryptosystem using bilateral-diffusion algorithm with dynamical compound chaos. The original image encryption scheme employed a compound chaotic function and (linear feedback shift register) LFSR. Experimental results of the studied scheme showed that it is strong enough to resist against different attacks. The method used in the cryptosystem under study, presents weakness and a chosen plaintext attack can be done to recover the plain image without any knowledge of the key value. Only one pair of (plaintext/cipher text) is needed to totally break the cryptosystem.

PL

W artykule zaproponowano atak na kryptosystem wykorzystujący algorytm bilateral-diffusion z dynamiczna składową chaosu. Pokazano że jest możliwe wystarczająco mocny opór przeciwko różnym atakom. Jest więc możliwe odzyskanie obrazu.

11

Effect of linewidth enhancement factor (LEF) on routes to chaos in optically injected semiconductor lasers

Al-Hosiny N. M.

Optica Applicata

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2021

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Vol. 51, nr 4

621--632

EN

The effect of the linewidth enhancement factor (LEF) or α-factor on two common routes to chaos (mainly period-doubling and quasi-periodic routes) in optically injected semiconductor laser is theoretically investigated using bifurcation diagrams. The value of the LEF is slightly modified to examine the sensitivity of routes to chaos to any variation in the LEF. Despite the fact that LEF enhances chaos in the system, both routes are found to be highly insensitive to the variation in the LEF.

12

Dynamics, control, stability, diffusion and synchronization of modified chaotic Colpitts oscillator

Rasappan Suresh, Niranjan Kumar K. A.

Archives of Control Sciences

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2021

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Vol. 31, No. 3

731--759

EN

The purpose of this paper is to introduce a new chaotic oscillator. Although different chaotic systems have been formulated by earlier researchers, only a few chaotic systems exhibit chaotic behaviour. In this work, a new chaotic system with chaotic attractor is introduced. It is worth noting that this striking phenomenon rarely occurs in respect of chaotic systems. The system proposed in this paper has been realized with numerical simulation. The results emanating from the numerical simulation indicate the feasibility of the proposed chaotic system. More over, chaos control, stability, diffusion and synchronization of such a system have been dealt with.

13

Chaotic path planning for grid coverage using a modified logistic-may map

Petavratzis Eleftherios, Moysis Lazaros, Volos Christos, Nistazakis Hector, Muñoz-Pacheco Jesus Manuel, Stouboulos Ioannis

Journal of Automation Mobile Robotics and Intelligent Systems

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2020

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Vol. 14, No. 2

3--9

EN

A simple and efficient method for creating a motion trajectory is presented with an aim to achieve sufficient coverage of a given terrain. A chaotic map has been used in order that the motion trajectory should be unpredictable. The chaotic path generator which has been created, is used for implementing a robot’s movement in four and eight directions. The path generator is tested in various scenarios and the results are discussed. After thorough examination, the proposed method shows that the motion in eight directions gives better and very satisfactory results.

14

Image cipher applications using the elliptical curve and chaos

Silva-García Víctor Manuel, Flores-Carapia Rolando, Rentería-Márquez Carlos, Luna-Benoso Bejamín, Chimal-Eguía Juan Carlos

International Journal of Applied Mathematics and Computer Science

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2020

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Vol. 30, no. 2

377--391

EN

A novel symmetric cryptosystem of the substitution permutation network type is presented for image encryption in 14 rounds. An algorithm is developed to generate 15 keys to encrypt images where each key is the image size. These keys are calculated using an elliptic curve with a constant zero value. The proposed curve is non-singular, non-supersingular, nor trace one. Chaos is employed to find a generating element in a cyclic subgroup and it is produced using the logistic map equation. In addition, a 16 × 16 substitution box is constructed using both chaos and an algorithm that defines a bijective function. The following tools are used in order to measure the degree of randomness of the encrypted figures: entropy, correlation, the discrete Fourier transform and a goodness-of-fit test with the chi-square distribution. Furthermore, an image size variable permutation is applied in the first round, and its inverse in the fourteenth.

15

A new multi-stable chaotic hyperjerk system, its special features, circuit realization, control and synchronization

Pham Viet-Thanh, Vaidyanathan Sundarapandian, Volos Christos, Jafari Sajad, Kapitaniak Tomasz

Archives of Control Sciences

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2020

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Vol. 30, No. 1

23--45

EN

Researchers have paid significant attention on hyperjerk systems, especial hyperjerk ones with chaos. A new hyperjerk system with seven terms and two parameters is analyzed. Chaotic attractors as well as coexisting attractors are displayed by the hyperjerk system. Thus it is a new multi-stable chaotic hyperjerk system. Further properties of the proposed hyperjerk system such as circuit design and backstepping-based control and synchronization are reported.

16

A new 4-D hyperchaotic system with no equilibrium, its multistability, offset boosting and circuit simulation

Vaidyanathan Sundarapandian, Moroz Irene M., Sambas Aceng

Archives of Control Sciences

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2020

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Vol. 30, No. 3

575--597

EN

A new 4-D dynamical system with hyperchaos is reported in this work. It is shown that the proposed nonlinear dynamical system with hyperchaos has no equilibrium point. Hence, the new dynamical system exhibits hidden hyperchaotic attractor. An in-depth dynamic analysis of the new hyperchaotic system is carried out with bifurcation transition diagrams, multistability analysis, period-doubling bubbles and offset boosting analysis. Using Integral Sliding Mode Control (ISMC), global hyperchaos synchronization results of the new hyperchaotic system are described in detail. Furthermore, an electronic circuit realization of the new hyperchaotic system has been simulated in MultiSim software version 13.0 and the results of which are in good agreement with the numerical simulations using MATLAB.

17

Image encryption based on Chebyshev chaotic map and S8 S-boxes

Hussain Iqtadar, Anees Amir, Alkhaldi Ali Hussain, Aslam Muhammad, Siddiqui Nasir, Ahmed Rehan

Optica Applicata

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2019

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Vol. 49, nr 2

317--330

EN

The encryption of image data is artful as compare to others due to some special characteristics such as entropy, contrast, the correlation between the pixels, intensity, and homogeneity. During encryption process, it is conventionally not easy to manage these characteristics with non-chaotic cryptosystems. Therefore for the sake of strong encryption algorithms, in last decades many cryptographers have presented invulnerable schemes for image encryption based on the chaotic maps. This manuscript aims to propose a strong encryption scheme based on a symmetric group of permutation advanced encryption standard (AES) substitution boxes and modified Chebyshev map. Principally, the secret key depends upon the parameters of Chebyshev map to create confusion in the main image and is encrypted by the scheme made from the S8 AES S-boxes and chaotic map. By this procedure, one can obtain an encrypted image that is entirely twisted. The results of analyses showed that the presented image encryption is strong and invulnerable.

18

An Improved M-ary Modulation Scheme Based on Chaotic Dynamics

Abdullah Hikmat N., Sahar Asaad H., Saeed Thamir R.

Journal of Telecommunications and Information Technology

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2019

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nr 4

13--19

EN

This paper proposes an improved chaos-based M-ary modulation system. It reproduces deterministic chaotic dynamics to create M-ary non-coherent modulation. The proposed modulation system transmits data using autonomous chaotic sequences. It separates the chaotic dynamics through the use of interleavers and realigns them through the use deinterleavers. The simulation results show that the improved scheme overperforms its traditional counterpart. The degree of improvement grows as the M-ary order is increased, with a penalty of increased system complexity.

19

Intelligent Forecasting of Automatic Train Protection System Failure Rate in China High-speed Railway

Kang Renwei, Wang Junfeng, Cheng Jianfeng, Chen Jianqiu, Pang Yanzhi

Eksploatacja i Niezawodność

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2019

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Vol. 21, no. 4

567--576

EN

Intelligent and personalized dynamic maintenance and spare parts configuration of high-speed railway have been the main trend to guarantee the safety capability of trains. In this paper, a new Automatic Train Protection (ATP) system failure rate calculation method is proposed, and the delay time and embedded dimension are determined by C-C algorithm. Then the phase space is reconstructed from one-dimensional time series to high-dimensional space. Based on chaotic characteristics of failure rate, a short-term intelligent forecasting model of failure rate of ATP system is established. The actual failure statistics from 2010 to 2018 are used as samples to train and test the validity of the model. From prediction results, it shows that the proposed chaos prediction model has an accuracy of 99.71%, which is better than the support vector machine model. Through the intelligent prediction of failure rate, this paper solves the maintenance inflexibility and imbalance of supply and demand of spare parts configuration.

PL

Inteligentna i spersonalizowana dynamiczna konserwacja i konfiguracja części zamiennych pociągów kolei dużych prędkości stanowią ostatnio główny trend w zakresie zapewniania bezpieczeństwa pociągów. W niniejszym artykule zaproponowano nową metodę obliczania intensywności uszkodzeń systemu Automatycznej Ochrony Pociągu (ATP), a czas opóźnienia i wymiar zanurzenia określano za pomocą algorytmu CC. Następnie, przestrzeń fazową przekształcono z jednowymiarowego szeregu czasowego do przestrzeni wielowymiarowej. Opierając się na chaotycznych charakterystykach intensywności uszkodzeń, utworzono model krótkoterminowego inteligentnego prognozowania awaryjności systemu ATP. Do uczenia modelu i weryfikacji jego trafności wykorzystano rzeczywiste dane statystyczne dotyczące awarii pociągów z lat 2010–2018. Z wyników prognoz wynika, że proponowany model predykcji, oparty na teorii chaosu, cechuje się dokładnością na poziomie 99,71%, czyli wyższą niż model maszyny wektorów nośnych. Dając możliwość inteligentnej predykcji intensywności uszkodzeń, niniejsza praca rozwiązuje problem braku elastyczności w utrzymaniu ruchu pociągów oraz braku równowagi między podażą a popytem na części zamienne.

20

Application of modified chebyshev polynomials in asymmetric cryptography

Lawnik Marcin, Kapczyński Adrian

Computer Science

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2019

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Vol. 20 (3)

289--303

EN

Based on Chebyshov polynomials, one can create an asymmetric cryptosystem that allows for secure communication. Such a cryptosystem is based on the fact that these polynomials form a semi-group due to the composition operation. This article presents two new cryptosystems based on modifications of Chebyshev's polynomials. The presented analysis shows that their security is the same as in the case of algorithms associated with the problem of discrete logarithms. The article also shows methods that allow for the faster calculation of Chebyshev polynomials.