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Cell development from an undifferentiated stem cell to a differentiated one is essential in forming an organism. In this paper, various bifurcations of a stem cell during this process are studied using a model based on Furusawa and Kaneko’s hypothesis. Furusawa and Kaneko’s hypothesis tells that the gene expression of stem cells is chaotic. By developing to a differentiated cell, the gene expression in more order, which is the cause of losing pluripotency. In this model, the chaotic dynamics of gene expression in the stem cells become ordered during the developments. Various patterns and bifurcation points can be seen during development. The bifurcation points and their predictions during the process of cell development are studied in this paper. Some well-known critical slowing down indicators are used to show the variations of slowness during the cell’s development and predict the bifurcation points. It is vital since the unexpected changes of the state can cause a disaster. All of the indicators have a proper trend by approaching the bifurcation points and faring away.

In this research, the ship power system is studied with a fractional-order approach. A 2-D model of a two-generator parallel-connected is considered. A chaotic attractor is observed for particular parameter values. The fractional-order form is calculated with the Adam–Bashforth–Moulton method. The chaotic response is identified even for the order 0.99. Phase portrait is generated using the Caputo derivative approach. Wolf’s algorithm is used to calculate Lyapunov exponents. For the considered values of parameters, one positive Lyapunov exponent confirms the existence of chaos. Bifurcation diagrams are presented to analyze the various dynamical behaviors and bifurcation points. Interestingly, the considered system is multistable. Also, antimonotonicity, period-doubling, and period halving are observed in the bifurcation diagram. As the last step, a fractional-order controller is designed to remove chaotic dynamics. Time plots are simulated to show the effectiveness of the controller.

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).

In this paper, we introduce a novel 3D chaotic oscillator which shows megastability without any external excitation. Some important dynamical properties of the proposed novel system were derived and investigated. Data protection application and its security analysis were realized for electrophysiological signals such as ECG, EEG and EMG on a microcomputer. This paper includes both encryption and data hiding processes for high security. Also a user interface was developed. For the encryption process, random numbers were generated by the megastable chaotic oscillator. These random numbers were tested with NIST-800-22 test which is the most widely accepted statistical test suite. The encrypted electrophysiological signals were analyzed by entropy, differential attacks, histogram, correlation, initial condition sensitivity, etc. The results of the analysis have shown that the proposed two level security method can be used in many fields as mobile. The most important feature of this paper is that both encryption and data hiding processes were implemented for electrophysiological signals. The experimental results verify that the proposed method has high security and is suitable for the protection of vital electrophysiological signals.

A chaotic simple jerk system (SJS) that belongs to systems with self-excited and hidden attractors is introduced in this paper. The dynamics of the proposed SJS is analytically and numerically investigated. Interestingly, the influence of the time delay on the proposed chaotic SJS is studied. In addition, the physical existence of self-excited and hidden chaotic attractors found in the proposed SJS and in the time-delayed form of SJSs (TDSJSs) are verified by using Orcard-PSpice software. Finally, chaos synchronization of identical, unidirectional, coupled, proposed chaotic TDSJSs is also reported.

An autonomous five-dimensional (5D) system with offset boosting is constructed by modifying the well-known three-dimensional autonomous Liu and Chen system. Equilibrium points of the proposed autonomous 5D system are found and its stability is analyzed. The proposed system includes Hopf bifurcation, periodic attractors, quasi-periodic attractors, a one-scroll chaotic attractor, a double-scroll chaotic attractor, coexisting attractors, the bistability phenomenon, offset boosting with partial amplitude control, reverse period-doubling, and an intermittency route to chaos. Using a field programmable gate array (FPGA), the proposed autonomous 5D system is implemented and the phase portraits are presented to check the numerical simulation results. The chaotic attractors and coexistence of the attractors generated by the FPGA implementation of the proposed system have good qualitative agreement with those found during the numerical simulation. Finally, a sound data encryption and communication system based on the proposed autonomous 5D chaotic system is designed and illustrated through a numerical example.

The outbreak of the novel coronavirus (COVID-19), which was firstly reported in China, has affected many countries worldwide. To understand and predict the transmission dynamics of this disease, mathematical models can be very effective. It has been shown that the fractional order is related to the memory effects, which seems to be more effective for modeling the epidemic diseases. Motivated by this, in this paper, we propose fractional-order susceptible individuals, asymptomatic infected, symptomatic infected, recovered, and deceased (SEIRD) model for the spread of COVID-19. We consider both classical and fractional-order models and estimate the parameters by using the real data of Italy, reported by the World Health Organization. The results show that the fractional-order model has less root-mean-square error than the classical one. Finally, the prediction ability of both of the integer- and fractional-order models is evaluated by using a test data set. The results show that the fractional model provides a closer forecast to the real data.

Coexistence of attractors with different or same type, multistability, is a complex behavior in nonlinear systems. This feature makes these systems applicable but difficult to control. Besides multistability, some new systems show megastability, existence of infinite number of coexisting attractors. In this paper, two simple megastable systems are presented in details. Moreover, these systems show hyperchaotic behavior which is rare in these types of systems as previously proposed systems mostly show chaos and periodic responses. To show the properties of these systems, nonlinear analytical tools are used in this article.

This paper presents a novel simple 4-D dissipative autonomous hyperchaotic system with a saddle-point index-2 equilibrium point. The dynamics of the new system consists of nine terms with two nonlinear terms. Thus, the proposed system is one of the simplest 4-D hyperchaotic systems. The new system also shows multistability behavior for some range of its parameters. Bifurcation diagrams, Lyapunov spectrum, Kaplan-Yorke dimension, and phase plots are used to analyze the complex dynamical behavior of the system. The discrete-time equivalent of the presented hyperchaotic system is made by using the Euler algorithm for improving the embedded chaos-based engineering applications on FPGA. Then, the design of a novel TRNG having chaotic entropy seed has been performed utilizing FPGA-based 4-D hyperchaotic system structure. The Euler-based model in the creation phase on FPGA has been described using VHDL with 32-bit IEEE 754-1985 floating-point format. The designed hyperchaotic system and TRNG unit have been synthesized using Xilinx ISE Design Tools, and chip statistics obtained from place-and-route process have been presented by testing in the Virtex-6 FPGA chip of Xilinx family. The numbers generated in high data rates of 185.447 Mbit/s have been obtained with 370.894 MHz clock frequency for the implementation of the novel TRNG unit. In the last stage, randomness tests of the generated random numbers have been carried out and the generated random numbers have passed successfully all randomness tests.

In this paper, a chaotification method based on the internal perturbation model (IPM) is proposed. The single-perturbation and the multiple-perturbations are introduced. The Sine map is taken as an example. Moreover, this method can be generalized to high-dimensional maps that contain sine, no matter where the sine term is in the system equation. we further apply IPM to an integer-order and a fractional-order Sine-series map. For those new maps, the parameter space and FuzzyEn complexity are significantly extended while maintaining the topological structure of system. These complex behaviors and digital signal processing (DSP) implementation validate the effectiveness of IPM and make it have the potential of better secure communication and encryption.

Map-based neuronal models have received much attention due to their high speed, efficiency, flexibility, and simplicity. Therefore, they are suitable for investigating different dynamical behaviors in neuronal networks, which is one of the recent hottest topics. Recently, the memristive version of the Rulkov model, known as the m-Rulkov model, has been introduced. This paper investigates the network of the memristive version of the Rulkov neuron map to study the effect of the memristor on collective behaviors. Firstly, two m-Rulkov neuronal models are coupled in different cases, through electrical synapses, chemical synapses, and both electrical and chemical synapses. The results show that two electrically coupled memristive neurons can become synchronous, while the previous studies have shown that two non-memristive Rulkov neurons do not synchronize when they are coupled electrically. In contrast, chemical coupling does not lead to synchronization; instead, two neurons reach the same resting state. However, the presence of both types of couplings results in synchronization. The same investigations are carried out for a network of 100 m-Rulkov models locating in a ring topology. Different firing patterns, such as synchronization, lagged-phase synchronization, amplitude death, non-stationary chimera state, and traveling chimera state, are observed for various electrical and chemical coupling strengths. Furthermore, the synchronization of neurons in the electrical coupling relies on the network's size and disappears with increasing the nodes number.

Network performance of neurons plays a vital role in determining the behavior of many physiological systems. In this paper, we discuss the wave propagation phenomenon in a network of neurons considering obstacles in the network. Numerous studies have shown the disastrous effects caused by the heterogeneity induced by the obstacles, but these studies have been mainly discussing the orientation effects. Hence, we are interested in investigating the effects of both the size and orientation of the obstacles in the wave re-entry and spiral wave formation in the network. For this analysis, we have considered two types of neuron models and a pancreatic beta cell model. In the first neuron model, we use the well-known differential equation-based neuron models, and in the second type, we used the hybrid neuron models with the resetting phenomenon. We have shown that the size of the obstacle decides the spiral wave formation in the network and horizontally placed obstacles will have a lesser impact on the wave re-entry than the vertically placed obstacles.

In this paper, a multiscroll snap oscillator with hyperbolic tangent function is proposed. There is no limitation in the number of scrolls and it can be increased by proper choice of a specific function. The Lyapunov exponents of the proposed system are obtained to testify the chaotic behavior of the system. Fractional order multiscroll system is derived from its integer order model by using the Adams–Bashforth–Moulton algorithm. A new scheme is applied in order to investigate the synchronization of the multiscroll systems. The main objective of the paper is to propose a multiscroll attractor and show that the number of scrolls can be controlled by the only nonlinear function. Such systems are less investigated in the literatures and has many real time applications like image and voice encryption, random number generators, chaos based communication systems and so on.

Extreme multi-stability is a newly introduced property observed in nonlinear dynamical systems. Such systems have very rich dynamical solutions depending on both parameters and initial conditions. On the other hand, designing dynamical systems with special features related to their equilibria is of great interest. In this paper, a novel chaotic system with extreme multi-stability and a line of equilibrium is presented. Such systems are so infrequent. It also should be noted that this designed chaotic system belongs to the category of dynamical systems with hidden attractors. Complete dynamical properties of this new system are investigated. Also, by the assistance of FPGA and electronic circuit implementation, this system is implemented.

In this paper we modified the conventional Chua’s circuit with a non-ideal voltage-controlled memristor with a quadratic internal state. Dynamical behaviors of Modified Memristor based Chua’s Circuit (MMCC) are investigated and Stability of equilibrium points are discussed we have computed the volume contraction rate and proved the system is dissipative. The existence of positive Lyapunov exponent showed the chaotic attractor present in the system. We found many Literatures on dynamic analysis on memristor based Chua’s circuit but most of them are restricted to only Poincare maps and Lyapunov spectrum. We carried out bifurcation analysis, bifurcations attained by varying the circuit parameters when evolving on a fixed manifold, bifurcations attained by changing the initial conditions, and hence changing between different manifolds, for a fixed set of parameters, and bifurcations due to changing circuit parameters as well as manifolds. The circuit hold multistability, to check the existence of coexisting attractors and the interesting phenomena of antimonotonicity is identified in the circuit. These special properties shows the intricacy of the circuit, which is vital for secure communication. We successfully implemented MMCC for voice encryption and proved the effective usability of the system in engineering application.

In the paper, we futher consider a fractional-order system from a modified Chua's circuit system with the smooth degree of 3 proposed by Fu et al. Bifurcation analysis, multistability and coexisting attractors in the the fractional-order modified Chua's circuit are studied. In addition, microcontroller-based circuit was implemented in real digital engineering applications by using the fractional-order Chua's circuit with the piecewise-smooth continuous system. Center for Nonlinear Systems, Chennai Institute of Technology, India [CIT/CNS/2020/RD/058] This work is partially funded by Center for Nonlinear Systems, Chennai Institute of Technology, India vide funding number CIT/CNS/2020/RD/058. WOS:000623134800001 2-s2.0-85101881968

Megastable chaotic systems are somehow the newest in the family of special chaotic systems. In this paper, a new megastable two-dimensional system is proposed. In this system, coexisting attractors are in some islands, interestingly covered by megalimit cycles. The introduced two-dimensional system has no defined equilibrium point. However, it seems that the origin plays the role of an unstable equilibrium point. Therefore, the attractors are determined as hidden attractors. Adding a forcing term to the system, we can obtain chaotic solutions and coexisting strange attractors. Moreover, the effect of three different values of the forcing term’s amplitude is studied. The dynamical properties of the designed system are investigated using attractor plots, bifurcation diagrams, and Lyapunov Exponents diagram. Phase portraits of the novel megastable oscillator are presented by FPGA design. Xilinx system generator block diagrams of the proposed system and trigonometric functions are also presented.

Chaotic systems with cyclic symmetry are very rare and have been less discussed in the literature. Similarly, megastable oscillators, which can have a finite or infinite number of coexisting attractors, have also attracted researchers. We propose a class of cyclic symmetry oscillators with the megastable property with infinite coexisting attractors for the first time in the literature. Various dynamical properties of the proposed oscillators are discussed in detail. An application for the detection of a feeble signal by using the proposed circulant megastable oscillator is presented. Since chaotic oscillators are highly sensitive to a tiny change in the parameters or an external input to the oscillator, this property of the proposed oscillator is used for the detection of a feeble signal. Simulated results validate the effectiveness of the proposed application. After that, a new chaotic Sine-Cosine Algorithm (SCA) is developed using the randomness of megastable oscillators. Subsequently, this new chaotic sine-cosine algorithm is used to determine the PID controller parameters of time-delay systems concerning the objective function. As a result, the proposed chaotic sine-cosine algorithm presents better performance for time-delay systems when compared with the available algorithms in the literature. (c) 2021 Elsevier Ltd. All rights reserved. WOS:000670086700001 2-s2.0-85106914266

Reinforcement learning models require a choice rule for assigning probabilities to actions during learning. This chapter reviews work on a new choice rule based on an amplitude amplification algorithm originally developed in quantum computing. The basic theoretical ideas for amplitude amplification are reviewed, as well as four different simulation applications to a task with a predator learning to catch a prey in a grid world, and one application to human learning in a 4 arm bandit choice task. The applications reviewed in this chapter demonstrate that QRL can improve speed and robustness of learning compared to standard choice rules such as epsilon-greedy and softmax choice rules.

In this work, LQR method is proposed for controlling and synchronizing newly developed chaotic system. The developed 4-D chaotic system has been investigated via time series, phase portraits and bifurcation diagrams. Calculation of the gain of linear control has been designed by LQR method, which is an optimal control method. For understanding active controller’s impact on global asymptotic stability of synchronization and control errors, the Lyapunov function has been used. Numerical analyses have demonstrated to reveal the effectiveness of the applied active control method and the results have been discussed. Besides, the new chaotic system has been modeled utilizing FFANN architecture. As a result, the output response of FFANN converges to the real output response of 4-D new chaotic system obtained using Dormand–Prince numerical algorithm. The obtained good results make the hardware design in efficient manner. It has been performed using the network parameters from FFANN structure on FPGA in VHDL. The performed design can be used with high clock frequencies up to 166.3 MHz. In addition, PRNG has been implemented and synthesized using FFANN-based chaotic oscillator for Xilinx Virtex-6 FPGA chip. The output rate of the designed FFANN-based PRNG is 166.3 Mbps.

Memelements play an important part in the design of high density memory systems and low power memory. In this paper, we created a novel fractional-order chaotic circuit with a memristor and a memcapacitor with a linear inductor. The various dynamical properties of the fractional-order system are investigated by using some dynamic analysis methods like Lyapunov exponents and bifurcation after the numerical solution for the fractional-order system. In addition, to show the applicative advantages of the proposed chaotic system, we have realized about the synchronization of fractional-order chaotic systems and used it in secure communication systems first time in the literature according to our knowledge. The results of the theoretical analysis and simulation show that the simple fractional-order chaotic system has very rich dynamic properties and can be used in different engineering applications. (c) 2021 Elsevier Ltd. All rights reserved. Sakarya University of Applied Science Scientific Research Projects Coordination Unit (SUBU BAPK) [2020-01-01-011]; Scientific and Technological Research Council of Turkey (TUBITAK)Turkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [2211-C] This work was supported by Sakarya University of Applied Science Scientific Research Projects Coordination Unit (SUBU BAPK, Project Number: 2020-01-01-011) . The author, Muhammed Ali PALA, is grateful to The Scientific and Technological Research Council of Turkey for granting a scholarship (TUBITAK, 2211-C) for him Ph.D. studies. WOS:000701870200005 2-s2.0-85113278977

Memristor-based oscillators are of recent interest, and hence, in this paper, we introduce a new Wien bridge oscillator with a fractional-order memristor. The novelty of the proposed oscillator is the multistability feature and the wide range of fractional orders for which the system shows chaos. We have investigated the various dynamical properties of the proposed oscillator and have presented them in detail. The oscillator is then realized using off-the-shelf components, and the results are compared with that of the numerical results. A combination synchronization scheme is proposed which uses more than one driver systems to synchronize with one response system. Indeed, we use two different techniques where the first one consists of splitting the transmitted signals into two parts where each part is loaded in different drive systems, while the second one consists of dividing time into different intervals and loading the signals in different drive systems. Such techniques improve the antiattack capability of the systems when used for secure communication.

The nonlinear dynamics of an incommensurate fractional-order single-machine infinite-bus (SMIB) power system benchmark model are explored and studied by means of modern nonlinear analysis theories, such as bifurcation, chaos, power spectral density (PSD), and bicoherence methods. The effect of incommensurate order derivatives on power system dynamics is presented. The study reveals that the power system undergoes interesting dynamics such as periodic motion, chaotic oscillations, and multistability whenever the system parameter values fall into particular ranges. A new fractional-order linear augmentation-based control scheme is applied to damp out the power system’s chaotic oscillation, change the stability of the coexisting states, and drive the system from multistability to monostability. The stability of the proposed control system is derived using Lyapunov theory. Simulation results confirmed the effectiveness and robustness of the proposed control scheme in damping power system oscillations and achieving good overall performance. The results in this paper will give a better understanding of the nonlinear dynamic behaviors of the incommensurate fractional-order SMIB power system.

An amplitude controllable hyperjerk system is constructed for chaos producing by introducing a nonlinear factor of memristor. In this case, the amplitude control is realized from a single coefficient in the memristor. The hyperjerk system has a line of equilibria and also shows extreme multistability indicated by the initial value-associated bifurcation diagram. FPGA-based circuit realization is also given for physical verification. Finally, the proposed memristive hyperjerk system is successfully predicted with artificial neural networks for AI based engineering applications.

Recently, megastable systems have grabbed many researchers’ interests in the area of nonlinear dynamics and chaotic systems. In this paper, the oscillatory terms’ coefficients of the simplest megastable oscillator are forced to blink in time. The forced system can generate an infinitive number of hidden attractors without changing parameters. The behavior of these hidden attractors can be chaotic, tori, and limit cycle. The attractors’ topology of the system seems unique and looks like picture frames. Besides, the existence of different coexisting attractors with different kinds of behaviors reflects the system's high sensitivity. Using the sample entropy algorithm, the system’s complexity for different initial values is assessed. In addition, the circuit of the introduced forced system is designed, and the possibility of implicating the system with analog elements is investigated.

Health monitoring is considered as a gigantic problem in emerging nations, particularly in inaccessible region. The development in radio telecommunication has upgraded the smart hospital in voluminous aspects. One of the visions of 5G communication systems is to deliver a dependable, protected and fast radio at anyplace and anytime for the forthcoming smart health care. To realize this, the 5G system must attained low peak to average power ratio (PAPR), efficient spectrum, small latency and faster data-rate. In the present correspondence, our work mainly focused to introduce a novel PAPR reduction technique, which is one of the necessities of 5G based smart hospital. Artificial intelligence (AI) based genetic algorithm (GA) supported selective mapping Sequence (SLM), known as GA-SLM is suggested to diminish the PAPR of the NOMA system. However, the required multiplications and additions for SLM techniques are too much, which increase the complexity of the system. Hence, it important to proposed AI techniques to minimize the intricacy. The investigation outcomes indicate that the efficiency of the GA-SLM outperforms the typical PAPR procedures.

In this paper, a new jerk system is designed. This system can display different characters of equilibrium points according to the value of its parameters. The proposed nonlinear oscillator can have both self-excited and hidden attractors. Dynamical properties of this system are investigated with the help of eigenvalues of equilibria, Lyapunov exponents' spectrum, and bifurcation diagrams. Also, an electronic circuit implementation is carried out to show the feasibility of this system. As an engineering application of this new chaotic jerk system, a chaotic communication system is realized by correlation delay shift keying. When the results of the communication system are examined, the transmitted information signal is successfully obtained in the receiving unit, and its performance efficiency is investigated in the presence of additive white Gaussian noise.

A simple jerk system with only one exponential nonlinearity is proposed and discussed. Dynamic analysis of the integer-order jerk system shows the existence of chaotic oscillations. A model for the fractional-order jerk system is derived. The Adomian decomposition method is used to analyse the fractional-order jerk system. Stability analysis of the fractional-order jerk system shows that chaotic oscillations exist in orders less than one and bifurcation analysis shows the range of fractional orders for periodic and chaotic oscillations. To show the randomness of the fractional-order jerk system, a pseudorandom number generator is designed and tested. The NIST-800-22 tests show that the proposed fractional-order jerk system is effective in showing randomness. Finally, an image hiding application to the audio data has been realized by using the developed RNG algorithm. The encrypted image is hidden by being embedded in the audio data, and then, on the receiver side, the data are recovered by taking the image data from the hidden audio file.

When revising the polarity and amplitude information in the feedback, a unique hypogenetic jerk system was obtained which has two controllers to switch the equilibria between stable and unstable. After providing some basic dynamical analysis, an electronic circuit was implemented, and the phase trajectory in the oscilloscope agrees with the numerical simulation. Further exploration shows that this unique chaotic system has superior performance as a random number generator or in voice encryption application.

In the field of genetics, it is well known that a specific genetic behavior may be influenced by more than one gene. There is a similar concept in genetic algorithms (GAs), called epistasis, which is the interaction between genes. This study demonstrates that, in spite of what is generally assumed, GAs are not an efficient optimization tool. This is because the main operator, mating (crossover), cannot function properly in epistatic optimization problems. In non-epistatic problems, although a GA can possibly provide a correct solution, it is an inefficient and time-consuming algorithm. As proof, we used conventional test functions and introduced new ones and confirmed our claim with simulation results.

Parameter identification (PI) is very important in system analysis and controller design and has wide applications in industry. PI is an essential step in designing mathematical models of the dynamical systems based on the measured data. Identification of chaotic systems is very challenging due to the butterfly effect. Recently, a state-space-based cost function based on Gaussian mixture model (GMM) has been proposed for the PI of the chaotic systems. In there, a GMM as a statistical model of the measured data modeled static features of the chaotic attractors in the state space. In this paper, we propose a new method which incorporates static and dynamic features in the GMM modeling in order to achieve a better cost function for the PI problem. The proposed method can extract suitable information from the trajectory of the chaotic attractor. We conduct some experiments for one-dimensional PI. Using measured data from 4D and 3D chaotic systems, empirical results indicate success of the proposed method.

Neural network is important for a wide range of applications. Especially, a small neural network can display various complex behaviors. In this work, the investigations of a Hopfield neural network and its field programmable gate array (FPGA) implementation have been reported. The considered Hopfield neural network is simple because it includes only three neurons. It is interesting that we observed chaos and numerous coexisting attractors in such a network. In addition, the network has been implemented via an FPGA platform to verify its feasibility.

In the last decades, many studies have been done about nervous system from the mathematical and computational point of view. Many mathematical models have been proposed to describe neuron. Most of them have described the membrane potential of a neuron in terms of the leakage current and the synaptic inputs. Very recently, according to the Maxwell electromagnetic induction theorem, researchers proposed a new neuron model which considers inner magnetic fluctuation and external electromagnetic radiation as a significant missing part that can participate in neural activity. In this paper, dynamical properties of this new model, such as equilibria and its stability, phase portraits, bifurcation diagram, Lyapunov exponents, and basin of attraction, are investigated. Moreover, an implementation of electronic circuit and FPGA is also done to verify the feasibility of the theoretical model.

Chaotic and hyperchaotic systems with interesting behaviors have been of interest in the recent years. In this paper we introduce a hyperchaotic memristor oscillator which shows both stable and unstable fixed points. Such systems have been less investigated in the literatures. It should also to be noted that the proposed hyperchaotic system has only one nonlinearity which is a flux controlled memristor. Depending on the control parameter, the system displays different behaviors and coexisting attractors. A linear quadratic regulator based synchronization of the proposed hyperchaotic system is designed and numerically analyzed. We also design such a fuzzy based PID controller for chaos control in such a memristor oscillator.

Discovering chaotic systems with interesting features has been of interest in the recent years. One such important and interesting feature is the type and shape of equilibrium points. We introduce a class of chaotic systems which could show different types of infinite equilibrium points. The fundamental properties of the proposed systems like bifurcation diagram and Lyapunov exponents are investigated. An electronic circuit of the presented chaotic systems is implemented. In addition, a chaos-based communication application by the differential chaos shift keying method with the new chaotic system is designed and tested for engineering application. According to the design test results, the proposed chaos-based communication system is successful. Therefore, the new chaotic system can be used in chaos-based communication systems.

It is well known in the market that the copper rotor motor can give good efficiency at par with the new era motors, and can handle higher temperatures to qualify for electric vehicle application. Being a heavy metal, die-cast copper rotor manufacturing needs absolute care for faithful rotor production. In this paper, the common faults in copper die-cast processing are identified and sufficient monitoring methods are suggested in a three-stage inspection. The final stage consists of a rotor quality test system, which detects most of the problems found in copper die-cast rotors. This rotor quality test system analysis helps to optimize the rotor manufacturing process and avoid the circumstances of fitting an inferior rotor in the motor assembly.

In this paper, we report a novel chaotic snap oscillator with one nonlinear function. Dynamic analysis of the system shows the existence of bistability. To study the time delay effects on the proposed snap oscillator, we introduce multiple time delay in the fourth state equation. Investigation of dynamical properties of the time-delayed system shows that the snap oscillator exhibits the same multistable properties as the nondelayed system. The new multistable hyperjerk chaotic system has been tested in chaos shift keying and symmetric choc shift keying modulated communication designs for engineering applications. It has been determined that the symmetric chaos shift keying modulated communication system implemented with the new chaotic system is more successful than the chaos shift keying modulation for secure communication. Also, circuit implementation of the chaotic snap oscillator with tangent function is carried out showing its feasibility.

In this paper, we report a new chaotic jerk system which shows self-excited and hidden oscillations depending on its parameters. Dynamic analysis shows that the proposed system exhibits multi-stability and coexisting attractors. To study the effect of time delays on the multi-stability feature of the system, we introduce multiple time delays in the third state variable. Investigation of dynamical properties of the time-delayed system shows the disappearance of multi-stability. Such a feature has not been reported earlier in the literatures.

In this note, we deal with parameter estimation methods of chaotic systems. The parameter estimation of the chaotic systems has some significant issues due to their butterfly effects. It can be formulated as an optimization problem and needs a suitable cost function. In this paper, we propose a new cost function based on a hidden Markov model which is a statistical tool for modeling of time series data. It can model dynamical characteristics of the chaotic systems. Moreover, the use of dynamical features of their strange attractors is investigated to achieve a better cost function in the procedure of parameter estimation. Our experimental results indicate the success of the proposed cost function in the one-dimensional parameter estimation of a new four-dimensional chaotic system and Lorenz system as a well-known three-dimensional chaotic system.

In this paper, we discuss how chaotic systems show the importance of imperfection. This happens through the butterfly effect. Then we discuss that chaotic systems with extreme multi-stability can much better demonstrate such importance. The reason is that in such systems not only the quantity of time-series is affected by butterfly effect, but also the quality of time-series is changed by small imperfections in parameters or initial conditions. We prove the importance of that difference better by comparing the efficiency of a newly proposed parameter estimation method on both an ordinary chaotic system and a chaotic system with extreme multi-stability.

Memristor-based chaotic and hyperchaotic systems are of great interest in the recent years, and addition of meminductor and memcapacitors to the family has widened the applications. In this paper, we propose a new chaotic system with fractional-order memristor and memcapacitor components. Nonlinear chaotic properties of the proposed system are investigated with equilibrium points, eigenvalues, Lyapunov exponents, bifurcation and bicoherence plots. We show that a small model disturbance can make the system to show self-excited and hidden attractors. We use the Adomian Decomposition method for implementing the proposed system in Field Programmable Gate Arrays.

Designing and analyzing new nonlinear dynamic systems have gotten much interest and effort among scientist recently. Between these approaches, chaotic and fractional-order systems have specific position as they can describe real phenomenon more accurate than the classical methods. In this article, a new chaotic system with specific topological properties has been introduced and also fractional version of this chaotic system has been developed. Different analytical methods like statistical, bifurcation and bicoherence analyses have been done to show properties of the proposed system. Field programmable gate arrays (FPGAs) implementation of chaotic and fractional-order system is another new topic which have been done in this article to show the feasibility of the proposed fractional-order system.

This work proposes a one-dimensional chaotic map with a simple structure and three parameters. The phase portraits, bifurcation diagrams, and Lyapunov exponent diagrams are first plotted to study the dynamical behavior of the map. It is seen that the map exhibits areas of constant chaos with respect to all parameters. This map is then applied to the problem of pseudo-random bit generation using a simple technique to generate four bits per iteration. It is shown that the algorithm passes all statistical NIST and ENT tests, as well as shows low correlation and an acceptable key space. The generated bitstream is applied to the problem of chaotic path planning, for an autonomous robot or generally an unmanned aerial vehicle (UAV) exploring a given 3D area. The aim is to ensure efficient area coverage, while also maintaining an unpredictable motion. Numerical simulations were performed to evaluate the performance of the path planning strategy, and it is shown that the coverage percentage converges exponentially to 100% as the number of iterations increases. The discrete motion is also adapted to a smooth one through the use of B-Spline curves.

In this paper, we investigate a four dimensional autonomous Van der Pol–Duffing (VdPD) oscillator which is built by converting an autonomous two-dimensional VdPD oscillator to a snap oscillator. The basic dynamical properties of the proposed autonomous VdPD snap oscillator are discussed in terms of its parameters by using standard tools of nonlinear analysis. The bifurcation analysis reveals rich and interesting features of the proposed autonomous VdPD snap oscillator such as period-doubling bifurcations, bistabe chaotic behavior, double scroll chaotic behavior, periodic windows, symmetry breaking and recovering bifurcations. One of the main findings of this paper is the presence of a window in the parameter space in which the proposed autonomous VdPD snap oscillator displays the striking feature of coexisting of multiple attractors. An electronic circuit model of the proposed autonomous VdPD snap oscillator is designed and its simulations are performed using an ORCAD-PSpice software. A good qualitative agreement is obtained between the numerical and ORCAD-PSpice results. Adaptive sliding mode control method is successfully used to achieve the synchronization of unidirectional coupled proposed autonomous VdPD snap oscillators in double scroll chaotic regime. Finally using LabVIEW, chaotic synchronization of unidirectional coupled proposed autonomous VdPD snap oscillators is used to develop and implement a real-time image encryption algorithm with a secondary image based on chaos masking technique.

There have been many different investigations of nonlinear dynamical systems. In this paper, we introduce a new chaotic system. In the proposed system, the attractor can be modified by adding a nonlinear term to the third state equation, thereby generating six different self-excited chaotic attractors. Some dynamical properties such as Hopf bifurcation, bifurcation diagrams, and multistability of the proposed system are investigated. The new system shows topologically different attractors for all six cases. We investigate two cases in depth. We also use nonlinear feedback control to drive the system to equilibrium, using two cases for illustration. Qatar National-Library The publication of this article was funded by the Qatar National-Library.

Chaos is often observed in forced nonlinear electrical circuits with saturable reactors. Simplest of such a circuit is presented and investigated in both integer order and non-integer (fractional) order form. For numerical analysis of fractional order system, the Adam-Bashforth-Moulton method is used. Some dynamic properties of the novel system are investigated. For implementing the system in field programmable gate arrays (FPGA), the Adomian decomposition method is used. Power and resource utilization of the fractional order system for implementing in FPGA are presented. Also, in this work, a novel fractional based sound encryption application is implemented as a unique application. Sakarya University Scientific Research Projects UnitSakarya University [2017-09-00-010] This work is supported by Sakarya University Scientific Research Projects Unit under Grants 2017-09-00-010.