Christos Volos

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• Ph.D.
• Professor (Full) at Aristotle University of Thessaloniki

Chaotic systems are nonlinear dynamical systemswhich are very sensitive to even small changes in the initial conditions. The control of chaotic systems is to design state feedback control laws that stabilize the chaotic systems around the unstable equilibrium points. This work derives a general result for the global chaos control of novel chaotic s...

A new memristive system is presented in this paper. The peculiarity of the model is that it does not display any equilibria and exhibits periodic, chaotic, and also hyperchaotic dynamics in a particular range of the parameters space. The behavior of the proposed system is investigated through numerical simulations, such as phase portraits, Lyapunov...

In this paper a new no-equilibrium hyperchaotic system is proposed by adding a tiny perturbation to a known hyperchaotic system with a line equilibrium. The fundamental dynamical properties of the new system are discovered including Lyapunov exponents, bifurcation diagram, Poincaré map and limit cycles. In addition, an electronic circuit emulating...

This paper introduces a new no-equilibrium chaotic system that is constructed by adding a tiny perturbation to a simple chaotic flow having a line equilibrium. The dynamics of the proposed system are investigated through Lyapunov exponents, bifurcation diagram, Poincaré map and period-doubling route to chaos. A circuit realization is also represent...

Antimonotonicity, i.e. forward period-doubling bifurcation sequences followed by reverse period-doubling sequences, as a parameter is varied in a monotone way, is observed in a FitzHugh – Nagumo type circuit, with a nonlinear resistor, which has a smooth cubic characteristic. The FitzHugh – Nagumo type electrical nonlinear oscillators simulate neur...

This work proposes a generalization of the family of chaotic maps without fixed points, proposed by Jafari et al.; 2016 and termed the Vertigo maps. The original map family is parameterized by four control parameters, which can be used to scale the function used as a seed and control its domain. Several theoretical results are provided regarding th...

This work provides a thorough review on the research topic of chaotification for discrete-time systems. Chaotification refers to the process of designing new chaotic maps, using existing maps from the literature as seed functions, with the goal of achieving a more complex behavior. This problem is of great theoretical interest, but also of practica...

This manuscript introduces a simple third-order Hopfield neural network. Its dynamics, implementation with a microcontroller and application to random number generation are explored. The model includes three coupled neurons with no synaptic weights between the first neuron and the third, and between the third and the second. The fundamental feature...

In this work, a comparison of Greek Orthodox religious chants is performed using fuzzy entropy. Using a dataset of chant performances, each recitation is segmented into overlapping time windows, and the fuzzy entropy of each window in the frequency domain is computed. We introduce a novel audio fingerprinting framework by comparing the variations i...

This study presents a novel approach by implementing an active memristor in a hyperchaotic discrete system, based on a cubic map, which is implemented by using two different microcontrollers. The key contributions of this work are threefold. The use of two microcontrollers with improved characteristics, such as speed and memory, for faster and more...

In this work, the use of false chaotic attractors in enhancing the security of chaos-based encryption applications will be explored. False attractors result by rearranging the solution trajectories of a nonlinear dynamical system, leading to novel shapes in the 3D space. This way, a single solution trajectory of a chaotic system can be used to gene...

In this work, the use of false chaotic attractors in enhancing the security of chaos-based encryption applications will be explored. False attractors result by rearranging the solution trajectories of a nonlinear dynamical system, leading to novel shapes in the 3D space. This way, a single solution trajectory of a chaotic system can be used to gene...

Chaotic random bit generators have become an integral part of chaotic cryptography and other data protection applications, where they are used as sources of deterministic randomness, to secure an information signal. The performance of the generator though will be heavily affected by the chaotic system that is chosen. The statistical performance, ke...

The Journal of Innovative Applied Mathematics and Computational Sciences (JIAMCS) is pleased to present Volume 2, Issue 2, featuring a carefully curated collection of eight research articles that contribute to the development of applied mathematics and scientific computing. This issue reflects the journal’s steadfast dedication to fostering schola...

https://dergipark.org.tr/en/pub/chaos/issue/88057

Memristors have become important components in artificial synapses due to their ability to emulate the information transmission and memory functions of biological synapses. Unlike their biological counterparts, which adjust synaptic weights, memristor-based artificial synapses operate by altering conductance or resistance, making them useful for en...

Chaotic systems with conditional symmetry have been proven to be greatly efficient for chaotic outcomes and regulation. Offset boosting hidden in an absolute value function not only provides a new possibility for polarity balance but also returns suitable feedback for chaos generation. It has been verified that a conditional symmetric system exhibi...

https://www.mdpi.com/journal/symmetry/special_issues/B2I4DHO848 This SI is devoted to issues related to robust chaos. It also concerns so-called chaotification methods, i.e., techniques for improving the properties of existing chaotic systems or constructing new systems with chaotic behavior. In addition, this SI will be of particular interest to...

https://dergipark.org.tr/en/pub/chaos/issue/86422

The Journal of Innovative Applied Mathematics and Computational Sciences (JIAMCS) is a peer-reviewed, open-access international journal, published semiannually by the University Center Abdelhafid Boussouf in Mila, Algeria. JIAMCS is dedicated to disseminating high-quality original research and comprehensive review articles across various fields, in...

Fractional-order (FO) chaotic systems exhibit richer and more complex dynamic behaviors compared to integer-order ones. This inherent richness and complexity enhances the security of FO chaotic systems against various attacks in image cryptosystems. In the present study, a comprehensive examination of the dynamical characteristics of the fractional...

This work proposes a family of modulo-based one-dimensional maps with three control parameters. The input to the modulo function includes the addition of three terms, the map’s previous value, a scalar, and a multiple of a chosen seed function. Under certain conditions, the proposed maps will have no equilibria, which brings them into the category...

https://dergipark.org.tr/en/pub/chaos/issue/83761

Chaos-based random bit generators are abundantly used in chaos-based encryption and security applications, as a fast, deterministic source of randomness, to perform actions like permutation and substitution. The chaotic map used as a source of randomness though may heavily affect the bit generator’s statistical randomness, key space, and speed. Thu...

This paper presents a new method of generating chaotic maps that do not have fixed points. The method uses an appropriate transformation of functions defined on the unit square in such a way that the newly created projection has no fixed points. In this way, countless new chaotic mappings can be created, both piecewise linear and nonlinear, that be...

In general, the construction of observers for nonlinear descriptor systems depends on the solvability of a linear matrix inequality involving system matrices, and it is based on the system’s nonlinearity. Therefore, the type of nonlinearity present in the system heavily affects the observer design process. There are significant developments in the...

The emergence of memristors has piqued significant interest in memristive maps due to their unique characteristics. In this paper, we introduce a novel and effective method for constructing memristor maps, leveraging the power of exponential units. Interestingly, the incorporation of these exponential units disrupts symmetry and alters the count of...

The understanding of nonlinear dynamics requires a solid background on differential equations, calculus, and numerical analysis. This is why the teaching of nonlinear dynamics and chaos is integrated in the later years of most curriculums of University Departments in the natural sciences. With chaotic systems being so abundant in real life though,...

The present study delves into the chaotic behavior of a non-ideal, vibrating system. The system is a mechanical setup, composed of a mass-spring-damper structure with cubic stiffness and an external excitation from a power-limited DC electric motor, driven by an unbalanced rotating mass causing the non-ideal excitation [1-3]. The dynamical behavior...

This work presents a numerical method to color the bifurcation diagram of any discrete map, based on the distribution of the map’s values in its domain. This density-colored diagram reveals information on the uniformity of the map’s value distribution across its domain set, as a bifurcation parameter is increased. This diagram can serve as a comple...

Chaos-related applications are abundant in the literature, and span the fields of secure communications, encryption, optimization, and surveillance. Such applications take advantage of the unpredictability of chaotic systems as an alternative to using true random processes. The chaotic systems used, though, must showcase the statistical characteris...

https://dergipark.org.tr/en/pub/chaos/issue/80150

In this work, a novel memristive Chua’s oscillator circuit is presented. In the proposed circuit, a linear negative resistor, which is parallel coupled with a first-order memristive diode bridge, is used instead of the well-known Chua’s diode. Following this, an extensive theoretical and dynamical analysis of the circuit is conducted. This involves...

Days of Applied NOnlinearity and Complexity (DANOC) is a two days online conference that intends to advance the discussion about the recent developments in nonlinearity and complexity, to creatively link applications and theory, tο explore the edge between different nonlinear scientific fields. We aim for DANOC to become a platform where scientists...

We are thrilled to introduce the new scope of the Dynamics, a platform that will unravel the captivating world of diverse dynamics and their multifaceted applications [...]

https://www.mdpi.com/journal/electronics/special_issues/1U9840AGGS The aim of this Special Issue is to advance the developments on security-related applications of chaotic systems. The topics span any research related to addressing the use of chaotic systems in information masking, encryption, cryptanalysis, secure communications, as well as hard...

https://dergipark.org.tr/en/pub/chaos/issue/77246

The Journal of Innovative Applied Mathematics and Computational Sciences (JIAMCS) is an online open access, peer-reviewed semiannual international journal published by the University Center Abdelhafid Boussouf, Mila, Algeria. The journal publishes high-quality original research and review papers from various fields related to applied mathematics, s...

Numerous applications for music listeners, educators, DJs, and musicians have been created over the past decade as the field of Music Deep Learning has expanded. Evidently, the majority of works rely on training their architectures using well-established databases, which consist primarily of Western popular music genres. This creates a deficiency i...

In this work, a family of piecewise chaotic maps is proposed. This family of maps is parameterized by the nonlinear functions used for each piece of the mapping, which can be either symmetric or non-symmetric. Applying a constraint on the shape of each piece, the generated maps have no equilibria and can showcase chaotic behavior. This family thus...

http://danoc.physics.auth.gr/ Days of Applied NOnlinearity and Complexity (DANOC) is a two days online conference that intends to advance the discussion about the recent developments in nonlinearity and complexity, to creatively link applications and theory, tο explore the edge between different nonlinear scientific fields.

In this work, the design and implementation of an autonomous mobile robot that can cover given workspaces, is presented. The motion commands are produced by a bit sequence, which is created from the combination, through an XOR function, of two separate chaotic random bitstreams. The implementation of the proposed method is performed by a robotic pl...

https://www.youtube.com/@lanscom7572

https://dergipark.org.tr/en/pub/chaos/issue/75756

The discrete system serves an important role in mimicking collective dynamics found in continuous dynamical systems, which are relevant to many realistic natural and artificial systems. To investigate the dynamical transition of a discrete system, we employ three-dimensional sinusoidal discrete maps with an additional self feedback factor. Specific...

In this work, a chaotification technique is proposed for increasing the complexity of chaotic maps. The technique consists of adding the remainder of multiple scalings of the map’s value for the next iteration, so that the most- and least-significant digits are combined. By appropriate parameter tuning, the resulting map can achieve a higher Lyapun...

Over the last decade the use of chaos theory has been expanding to a plethora of applications related to engineering, physics, economics, lasers and communications. From the above, chaos based encryption and secure communications are among the most prominent ones. In these fields, chaotic systems are used as a deterministic source of entropy, in or...

A key challenge for drug dosing schedules is the ability to learn an optimal control policy even when there is a paucity of accurate information about the systems. Artificial intelligence has great potential for shaping a smart control policy for the dosage of drugs for any treatment. Motivated by this issue, in the present research paper a Caputo–...

In this chapter, the construction of an efficient method for a fast and complete scanning of a given area is presented. An additional aspect is the insertion of FitzHugh–Nagumo chaotic system in order to create random-like motions. Then, a modulo operator was used in the production of the necessary motion commands. For further improvement of the pr...

In this paper, a new chaotic memristor system is developed based on a well-known nonlinear circuit. By replacing the nonlinear positive conductance of Shinriki's circuit with a memristor emulator, the new simple chaotic circuit can reduce the number of active elements and reduce power consumption. An analysis of equilibria and stability, dissipativ...

The discipline of Deep Learning has been recognized for its strong computational tools, which have been extensively used in data and signal processing, with innumerable promising results. Among the many commercial applications of Deep Learning, Music Signal Processing has received an increasing amount of attention over the last decade. This work re...

https://dergipark.org.tr/en/pub/chaos/issue/73767

Many drawbacks in chaos-based applications emerge from the chaotic maps' poor dynamic properties. To address this problem, in this paper a chaotification model based on modulo operator and secant functions to augment the dynamic properties of existing chaotic maps is proposed. It is demonstrated that by selecting appropriate parameters, the resulti...

A chaotic navigation algorithm is designed for an autonomous agent, that has the objective of exploring a given area, whilst moving unpredictably. The algorithm uses the Renyi map as a randomness source to generate the orientation of the robot and the direction it can move. There are eight possible directions, but the motion is limited to only thre...

This topical issue collects contributions of recent achievements and scientific progress related to the collective behavior of nonlinear dynamical oscillators. The individual papers focus on different questions of present-day interest in this topic.

In 1971, Chua suggested that there should be a fourth electrical component in addition to resistor, capacitor and inductor. This new component was proposed to be called “memristor”. Due to lack of commercially available memristors many emulators are mainly used in nonlinear circuits. Also, the memristance functions are used in many dynamical system...

https://dergipark.org.tr/en/pub/chaos/issue/73033

In this work, we consider polynomial approximations of the sine map, which is known to be chaotic. The dynamics of the maps obtained for different orders of approximations are studied using classical tools. Comparison of the behavior is made through common bifurcation diagrams, 0–1 test results, Lyapunov exponent diagrams and approximate entropy di...

Currently, chaotic cryptography is mainly concentrated on image encryption. Once-popular stream-encryption algorithms, e.g., textual data, are now rarely considered. This article studies how chaotic image-encryption algorithms can be used to encrypt text. The proposed approach to this problem consists of two stages: in the first stage, the text mes...

This Issue is dedicated to some selected papers of the International Conference on Mathematics and Applications (ICMA'2021), held on December 7-8, 2021, at Blida 1 University, Algeria. Guest Editor: Mohammed Hachama Associet Editors: - Benbachir Maamar -Redouane Boudjemaa ARK: https://n2t.net/ark:/49935/jiamcs.v2i2 Published: 10-09-2022

This paper proposes a new one-dimensional chaotic map. The map consists of a coupling between two hyperbolic tangent terms, where the second term is delayed, to avoid dynamical degradation. The map is studied through computation of its bifurcation diagrams and Lyapunov exponent diagrams and is shown to have constant chaotic behavior for almost all...

Today, one of the most studied phenomena of nonlinear dynamical systems is Chaos [...]

In this work, a chaotification technique is proposed that can be used to enhance the complexity of any one-dimensional map by adding the remainder operator to it. It is shown that by an appropriate parameter choice, the resulting map can achieve a higher Lyapunov exponent compared to its seed map, and all periodic orbits of any period will be unsta...

Chaos theory is currently one of the most fascinating fields in modern science, revolutionizing our understanding of organization and patterns in nature [...]

This issue is dedicated to the memory of Prof. Tenreiro Machado. https://dergipark.org.tr/en/pub/chaos/issue/64884

A novel approach to the physical memristor’s behavior of the KNOWM is presented in this work. The KNOWM’s memristor’s intrinsic feature encourages its use as a nonlinear resistor in chaotic circuits. Furthermore, this memristor has been shown to act like a static nonlinear resistor under certain situations. Consequently, for the first time, the KNO...

In 1976, Prof. Leon Chua proposed that a physical thermistor can be modeled as a memristive device, which can be used as a nonlinear element in chaotic circuits. In this direction, an autonomous circuit with two passive elements (inductor and capacitor), a nonlinear resistor, and a thermistor, which plays the role of a nonlinear locally active memr...

This work introduces a novel chaotic map defined by composition of the quantum logistic map and the sine map. The dynamic behavior of this map is thoroughly investigated and is shown to be more complex than that of the original quantum logistic map. Sequentially, a PRBG is defined using the values of the introduced map, the validity of which is det...

During the fall semester of 2021-2022 academic year, a seminar series on ’Chaotic Cryptography’ was delivered at the Department of Computer Aided Design (CAD), St. Petersburg Electrotechnical University ’LETI’, Russia. The seminar aimed at introducing students to state of the art research topics that connect chaos theory to various applications rel...

This paper investigates the issue of chaos-based image encryption. A new one-dimensional piecewise chaotic map based on the z-shaped fuzzy number is proposed and investigated, exhibiting regions of constant chaos and high Lyapunov exponent values. A pseudorandom bit generator based on the novel chaotic map is designed and successfully passes the Na...

In this paper, a novel approach of the KNOWM’s physical memristor behavior is introduced. It has been experimentally observed that this memristor, under certain conditions, can behave as a static nonlinear resistor. This inherent property of the KNOWM’s memristor prompts its use as a nonlinear reistor in chaotic circuits. Therefore, in this work, f...

In the present study, the simulation of an immunotherapy effect for a known dynamical system, that describes the process for avascular, vascular, and metastasis tumor growth based on a chemical network model, has been presented. To this end, square signals of various amplitudes have been used, to model the effect of external therapy control, in ord...

Chaos-based secure communications is a broadly studied field in nonlinear dynamics. Such technique is traditionally based on chaotic synchronization between master and slave systems implemented as the transmitter and receiver. A common way to encode the message is switching the bifurcation parameters of the master system, which leads to perturbatio...

In the research on chaotic systems, which are used for cryptography and secure communication schemes, a key characteristic is the introduction of novel chaotic systems, usually by adding complexity to the existing ones in order to ensure security. In this direction, this chapter proposes novel chaotic systems, which are the composition of fuzzy num...

As shown by Leon Chua in 1976 a physical thermistor can be modeled as a memristive device. Later, Ginoux et al. designed a circuit with four elements, an inductor, a capacitor, a nonlinear resistor, and a thermistor, which plays the role of a nonlinear locally active memristor. In this work, the aforementioned autonomous circuit is modified to a no...