Chaotic Oscillations Research Articles

Compact grounded memristor model with resistorless and tunability features

This research article provides a circuit illustration of a grounded memristor emulator. An operational transconductance amplifier (OTA) is one of its active components, along with two transistors and one capacitor. With a simple flip of the input ports, the incremental and decremental settings for the proposed memristor may be preserved. With the capacity to function in the megahertz band, the circuit offers a resistorless and controllable feature. Using the Cadence Virtuoso EDA tool in an analog design environment (ADE), PSPICE simulation with 0.18 µm TSMC technology parameter has been used to illustrate the viability of the suggested memristor. It has been confirmed in the simulation section that the operating frequency and tunability responses in the current-voltage (I-V) plane are in reasonable agreement with the theory. The suggested memristor model’s resilience has also been tested using process corner, Monte Carlo analysis, and temperature analyses, as well as single and parallel connected structures. The suggested memristor model is simple and does not need additional sub-circuit components, making it appropriate for implementation in integrated circuits. The experimental demonstration has been carried out by making a prototype on a breadboard using ICs, which exhibits good agreement with theoretical and simulation results. Single/parallel combinations of memristor, chaotic oscillator, and high pass filter have been presented to demonstrate its application.

Dynamics of spin oscillation in double barrier synthetic antiferromagnet based magnetic tunnel junction in presence of spin-transfer torque

In this work, we have studied the spin dynamics of a synthetic antiferromagnet (AFM)/heavy metal/ferromagnet double barrier magnetic tunnel junction in the presence of Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction, interfacial Dzyaloshinskii–Moriya (iDM) interaction, Néel field, and Spin–Orbit Coupling (SOC) with different Spin-Transfer Torque (STT). We employ the Landau–Lifshitz–Gilbert–Slonczewski equation to investigate the AFM dynamics of the proposed system. We found that the system exhibits a transition from regular to damped oscillations with the increase in strength of STT for systems with a weaker strength of iDM interaction than RKKY interaction while displaying sustained oscillations for systems having the same order of RKKY and iDM interactions. On the other hand, the systems with sufficiently strong iDM interaction strength exhibit self-similar but aperiodic patterns in the absence of the Néel field. In the presence of the Néel field, the RKKY interaction dominating systems exhibit chaotic oscillations for low STT but display sustained oscillations under moderate STT. Our results suggest that the decay time of oscillations can be controlled via SOC. The system can work as an oscillator for low SOC but displays non-linear characteristics with the rise in SOC for systems having weaker iDM interaction than RKKY interactions. In contrast, opposite characteristics are noticed for iDM interaction dominating systems. We found periodic oscillations under low external magnetic fields in RKKY interaction dominating systems. However, moderate fields are necessary for sustained oscillation in iDM interaction dominating systems. Moreover, the system exhibits saddle-node bifurcations and chaos under moderate Néel field and SOC with suitable RKKY and iDM interactions. In addition, our results indicate that the magnon lifetime can be enhanced by increasing the strength of iDM interaction for both optical and acoustic modes.

FPGA Realization of an Image Encryption System Using a 16-CPSK Modulation Technique

Nowadays, M-Quadrature Amplitude Modulation (M-QAM) techniques are widely used to modulate information by bit packets due to their ability to increase transfer rates. These techniques require more power when increasing the modulation index M to avoid interference between symbols. This article proposes a technique that does not suffer from interference between symbols, but instead uses memory elements to store the modulation symbols. In addition, the aim of this paper is to implement a four-dimensional reconfigurable chaotic oscillator that generates 16-Chaotic Phase Shift Keying (16-CPSK) modulation–demodulation carriers. An encryption and modulation transmitter module, a reception module, and a master–slave Hamiltonian synchronization module make up the system. A 16-CPSK modulation scheme implemented in Field Programmable Gate Array (FPGA) and applied to a red-green-blue (RGB) and grayscale image encryption system are the main contributions of this work. Matlab and Vivado were used to verify the modulation–demodulation scheme and synchronization. This proposal achieved excellent correlation coefficients according to various investigations, the lowest being −15.9×10−6 and 0.13×10−3 for RGB and grayscale format images, respectively. The FPGA implementation of the 16-CPSK modulation–demodulation system was carried out using a manufacturer’s card, Xilinx’s Artix-7 AC701 (XC7A200TFBG676-2).

Mixed-mode oscillations and chaos in a complex chemical reaction network involving heterogeneous catalysis.

The nonlinear dynamical behavior in a complex isothermal reaction network involving heterogeneous catalysis is studied. The method first determines the multiple steady states in the reaction network. This is followed by an analysis of bifurcation continuations to identify several kinds of bifurcations, including limit point, Bogdanov-Takens, generalized Hopf, period doubling, and generalized period doubling. Numerical simulations are performed around the period doubling and generalized period doubling bifurcations. Rich nonlinear behaviors are observed, including simple sustained oscillations, mixed-mode oscillations, non-mixed-mode chaotic oscillations, and mixed-mode chaotic oscillations. Concentration-time plots, 2D phase portraits, Poincaré maps, maximum Lyapunov exponents, frequency spectra, and cascade of bifurcations are reported. Period-doubling and period-adding routes leading to chaos are observed. Maximum Lyapunov exponents are positive for all the chaotic cases, but they are also positive for some non-chaotic orbits. This result diminishes the reliability of using maximum Lyapunov exponents as a tool for determining chaos in the network under study.

Performance Evaluation of FPGA-Based Design of Modified Chua Oscillator

The chaotic systems are one of the most important areas that increasing the popularity and are actively used in several fields. One of the most essential structures in chaotic systems is chaotic oscillator which generates chaotic signals. IQ-Math and floating point number systems are one of the preferred number standards. Presented in this study, the Modified Chua chaotic oscillator has been designed to work on FPGA chips using fixed point and floating point number systems. Euler numeric algorithm has been used for the design of the Modified Chua chaotic oscillator. The first section of the study, Modified Chua chaotic system based on fixed point has been composed the model in the Matlab Simulink and transformed to VHDL with the help of Matlab HDL Coder Toolbox. The second section of the study, Modified Chua chaotic oscillator has been designed with VHDL based on floating point. Modified Chua chaotic oscillators which are composed with two different number standards have been tested using Xilinx ISE Design Tools in VHDL. Modified Chua chaotic oscillators which have two different numbers standards and designed, are synthesized for Virtex-6 on ML605 FPGA development board with Xilinx ISE Design Tools 14.2 program. Values that are achieved from the process of synthesizing and maximum operating frequency have been presented. As a result, the study has obtained that fixed point number standard maximum operating frequency is 50.242 MHz and floating point number standard maximum operating frequency is 273.631 MHz.

Does a Fractional-Order Recurrent Neural Network Improve the Identification of Chaotic Dynamics?

This paper presents a quantitative study of the effects of using arbitrary-order operators in Neural Networks. It is based on a Recurrent Wavelet First-Order Neural Network (RWFONN), which can accurately identify several chaotic systems (measured by the mean square error and the coefficient of determination, also known as R-Squared, r2) under a fixed parameter scheme in the neural algorithm. Using fractional operators, we analyze whether the identification capabilities of the RWFONN are improved, and whether it can identify signals from fractional-order chaotic systems. The results presented in this paper show that using a fractional-order Neural Network does not bring significant advantages in the identification process, compared to an integer-order RWFONN. Nevertheless, the neural algorithm (modeled with an integer-order derivative) proved capable of identifying fractional-order dynamical systems, whose behavior ranges from periodic and multi-stable to chaotic oscillations. That is, the performances of the Neural Network model with an integer-order derivative and the fractional-order network are practically identical, making the use of fractional-order RWFONN-type networks meaningless. The results deepen the work previously published by the authors, and contribute to developing structures based on robust and generic neural algorithms to identify more than one chaotic oscillator without retraining the Neural Network.

Complex dynamics in an atmospheric pressure glow discharge in helium: transition from stationary to periodic oscillatory, and fully chaotic states

Abstract This work deals with the numerical study of spontaneous temporal oscillations in an atmospheric pressure glow discharge (APGD) in helium. The transition of helium APGD from stationary to periodic oscillatory state through the Hopf bifurcation, and further from periodic to chaotic oscillations through period-doubling bifurcations is explored. The choice of the discharge and external electric circuits parameters is guided by the relevant experiments. The ballast resistance and supply voltage of the external circuit play the role of control parameters. The method is based on the stability analysis of stationary states of the discharge. 

The stability diagram predicting parameter regimes at which stable and oscillatory states of the APGD can be expected is obtained. The effects of the discharge parameters (such as the gas gap, secondary electron emission coefficients, and capacitance in the external electric circuit) on the bifurcation curves are identified. 

The Lorenz map and corresponding period-doubling bifurcation diagram characterizing transition to chaotic oscillations in helium APGD with an increase in the control parameter are derived. The value of the capacitance in the external circuit plays a critical role in the dynamical behavior of the discharge. Decreasing its value contributes to the dissipation/damping of the system, whereas increasing it enhances the irregular behavior of the system.

Effects of Gain Saturation on Orbital Instability of Chaotic Laser Diode with External Pseudorandom Signal

In a laser diode (LD) system with optical injection, the effects of gain saturation of the LD on the orbital instability of the system are analyzed numerically. For the optical injection LD system without signal application, it is shown that the effect of optical injection is suppressed in the system with gain saturation and small optical injection, and that a higher amount of optical injection is necessary to obtain similar dynamics. Next, in the optical injection LD system with a pseudo-random signal applied to the LD drive current, it is confirmed that when the dynamics are a periodic window between chaotic and chaotic regions, chaotic dynamics are actualized as the standard deviation of the applied signal becomes larger. Furthermore, it is suggested that this phenomenon can be explained by linear stability analysis, and it is shown by introducing randomly varying tentative gain coefficients that gain fluctuations that lead to an expansion of the chaotic region. Hence, the results of this study provide research on the effects of gain saturation on chaotic oscillation in LDs with pseudo-random signals applied and contribute to the generation of more complex chaotic signals, chaotic secure communication, and random number generation.

Synchronization of Chaotic Systems with Huygens-Like Coupling

One of the earliest reports on synchronization of inert systems dates back to the time of the Dutch scientist Christiaan Huygens, who discovered that a pair of pendulum clocks coupled through a wooden bar oscillate in harmony. A remarkable feature in Huygens’ experiment is that different synchronous behaviors may be observed by just changing a parameter in the coupling. Motivated by this, in this paper, we propose a novel synchronization scheme for chaotic oscillators, in which the design of the coupling is inspired in Huygens’ experiment. It is demonstrated that the coupled oscillators may exhibit not only complete synchronization, but also mixed synchronization—some states synchronize in anti-phase whereas other states synchronize in-phase—depending on a single parameter of the coupling. Additionally, the stability of the synchronous solution is investigated by using the master stability function approach and the largest transverse Lyapunov exponent. The Lorenz system is considered as particular application example, and the performance of the proposed synchronization scheme is illustrated with computer simulations and validated by means of experiments using electronic circuits.

TWO-DIMENSIONAL HYPERCHAOTIC MAP FOR CHAOTIC OSCILLATIONS

This manuscript explores a two-dimensional hyperchaotic map for generating chaotic oscillations. Hyperchaotic maps are finding increasing applications in various scientific and technological fields due to the unique properties of their generated oscillations. The studied map, based on two interconnected piecewise-linear functions, is one of the simplest for generating oscillations with a predetermined distribution of values across a continuous parameter space. This simplicity allows for wide applicability in various contexts. The paper presents simulation results demonstrating control over the parameters of the dynamic modes. Building upon these modeling results, a two-dimensional hyperchaotic system is implemented using an electric circuit. The chosen map is attractive due to its inherent simplicity and ease of parameter control. By adjusting these parameters, the distribution of the generated signal's values can be manipulated. The circuit consists of two symmetrical sections connected via feedback loops, employing four amplifiers with variable gain. The gain values act as the circuit's implementation of the control parameters. Chaotic oscillations are generated by applying a delayed clock signal from an external square wave generator to circuit elements. The obtained experimental results exhibit excellent agreement with the simulation data.

Transition among oscillation death, amplitude death, and revival of oscillation in coupled time-delayed systems with diffusivity and common environment

In this paper, we study the transition between different oscillation suppression, revival of oscillation, and oscillatory states in time-delayed chaotic oscillators coupled through simultaneous diffusive and environmental coupling. The present paper, for the first time, reports the occurrence of oscillation death and nontrivial amplitude death states in coupled intrinsic time-delayed systems. Moreover, we explore the revival of the oscillations from these diverse oscillation suppression states. We analyze the stability of the coupled time-delayed system and through extensive numerical investigations, we delineate all the dynamical states in the parameter space. The study is extended to a network of time-delayed oscillators and identical transition scenarios have been obtained. Finally, we support our results in an electronic hardware circuit-based experiment and demonstrate that all the transition scenarios are robust enough in a real world system where the presence of noise, fluctuations, and parameter mismatch are inevitable.

Broadband chaotic signal generation with a solitary microcavity laser

We have proposed and experimentally demonstrated a novel chaotic signal generator using a solitary deformed square microcavity laser. The carrier density in the microcavity laser exhibits periodic or chaotic oscillation due to the interaction between the cavity modes, as long as the frequency difference between the modes is comparable to the relaxation oscillation frequency of the laser. The oscillation of carrier density leads to the variation of the Fermi level and, consequently, the applied voltage. The electrical signal can then be extracted directly from the electrode of the microcavity laser without the need for optical-electrical conversion. The obtained chaotic signal has a standard bandwidth of 9.6 GHz, and physical random numbers can be generated from the temporal waveform with simple post-processing methods. The scheme demonstrated here requires simple hardware, making it a promising solution for chaotic signal generators in various applications.

Chaotic systems based on higher-order oscillatory equations

This paper discusses the design process toward new lumped chaotic systems that originates in higher-order ordinary differential equations commonly used as description of ideal oscillators. In investigated third-order case, two chaotic oscillators were constructed. These systems are dual in the sense of vector field geometry local to fixed points. The existence of robust chaos was proved by both standard routines of numerical analysis and practical measurement. For the fourth-order oscillatory equation, the concept based on interaction between superinductor and supercapacitor was examined in detail. Since both “superelements” are active, the nonlinearity essential to the evolution of chaos is fully passive. It is demonstrated that complex motion is robust and does not represent long transient behavior or numerical artefact. The existence of chaos was verified using standard quantifiers of the flow, such as the largest Lyapunov exponents, recurrence plots, approximate entropy and sensitivity calculation. A good final agreement between theoretical assumptions and practical results will be concluded, on a visual comparison basis.

True Random Number Generator Based on Chaotic Oscillation of a Tunable Double-Well MEMS Resonator.

Chaotic systems have aroused interest across various scientific disciplines such as physics, biology, chemistry, and meteorology. The deterministic but unpredictable nature of a chaotic system is an ideal feature for random number generation. Microelectromechanical systems (MEMS) are a promising technology that effectively harnesses chaos, offering advantages such as a compact footprint, scalability, and low power consumption. This paper presents a true random number generator (TRNG) based on a double-well MEMS resonator integrated with an actuator and position sensor. The potential energy landscape of the proposed MEMS resonator is actively tunable with a direct current voltage. Experimental demonstrations of tunable bistability and chaotic resonance are reported in this paper. A chaotic time sequence is generated through piezoresistive sensing of the position of the MEMS resonator once it is driven into the chaotic regime. Subsequently, the randomness of the bit sequence, achieved by applying the exclusive or function to a digital chaotic sequence and its delayed differential is confirmed to meet the National Institute of Standards and Technology specifications. Moreover, the throughput and energy efficiency of the proposed MEMS-based TRNG can be adjusted from 50 kb s-1 and 0.44 pJ per bit at a low energy barrier to 167 kb s-1 and 6.74 pJ per bit at a high energy barrier by changing the MEMS device's potential well. The tunability of the proposed double-well MEMS resonator not only offers continuous adjustments in the energy efficiency of TNRG but also unveils vast and diverse research opportunities in analog computing, encryption, and secure communications.

A novel memristive chaotic jerk circuit and its microcontroller-based sliding mode control

Due to the experimental realization of memristor circuit elements, research on memristors and memristor-based circuits has surged. Because of their nonvolatile and nonlinear behavior, memristors can be easily applied to chaotic circuits. This study introduces a novel memristive 3D chaotic jerk system, comprising only seven terms, along with its electronic model and microcontroller-based control. The flux-controlled memristor-based jerk system exhibits complex dynamics, which were analyzed through various properties such as phase portraits, the Jacobian matrix, equilibria, eigenvalues, Lyapunov spectra, bifurcation diagrams, and transient chaos behavior. Three controllers, namely, nonlinear feedback, classical sliding mode, and integral sliding mode were designed to control the chaotic jerk oscillator. Lyapunov functions were used to synthesize the nonlinear feedback controller and ensure system stability with the sliding mode technique. Numerical tests under various performance criteria and disturbance conditions showed that the sliding mode controller outperforms the nonlinear feedback controller due to its single-state control structure. The chaotic jerk oscillator hardware circuit was designed and implemented, operating easily with initial conditions set to zero and low DC supply voltages, with all output voltages within ±6V. Both theoretical and simulation results demonstrate the system’s complexity and applicability, with experimental results aligning well with simulations. Consequently, effective microcontroller-based control was achieved using a single-state controller.

MOSFET-only Meminductor Emulator and its Application in Chaotic Oscillator

MOSFET-only Meminductor Emulator and its Application in Chaotic Oscillator

Positive semi-definite Lyapunov function-based adaptive control for nonlinear discrete-time systems with application to chaotic Duffing oscillator

Positive semi-definite Lyapunov function-based adaptive control for nonlinear discrete-time systems with application to chaotic Duffing oscillator

Spray swirling flame dynamic under combined modulation of air and fuel

Combustion instability is still a main challenge in developing advanced gas turbine combustors. It is essential to conduct instability control once it occurs. In this paper, liquid fuel modulation by a high-speed on/off valve is used to control flame oscillation generated by loudspeakers. Spray swirling flame dynamic under the combined modulation of air and fuel is experimentally studied. Flame dynamical characteristics and coherent structures at different excitation phase delays are discussed with nonlinear time-series analysis and proper orthogonal decomposition method. Experimental results show flame heat release rate fluctuation is decreased by 86% at 40° while flame instability is intensively enhanced at 220°. Phase portraits and recurrence plots show the flame is in a chaotic oscillation with low amplitude aperiodic oscillations at 40° while it suffers from the largest fluctuation at 220°. Difference in flame dynamic is caused by the destructive (out of phase) and constructive (in phase) interference of heat release rate fluctuations induced by air excitation and fuel modulation. Flame returns back to its nature dynamical behavior under out-of-phase modulation. Longitudinal modes of the spray flame are enhanced while the spiral modes are inhibited under in-phase modulation.

Synchronization of bowhead whales

Inferring animal behavior from irregular tracking data is a challenging area of research. It is particularly difficult to determine if whales, who intermittently explore different depths while staying in the same acoustic medium, synchronize their days with their prey and each other over kilometer-scale distances. Here, we aim to better understand the diving behavior of bowhead whales () in Disko Bay, West Greenland, using the largest high-frequency dive-depth dataset to date (144 days at 1 Hz from 12 different whales) and nonlinear dynamics, whereby we consider the whales to be chaotic (aperiodic) oscillators. We find that foraging whales dive deeper during the daytime in spring, with this diving behavior being in apparent synchrony with their vertically migrating prey. Furthermore, we demonstrate that bowhead whales can synchronize their behavior with each other for up to a week while staying within a range of up to ∼100km. This discovery agrees with the acoustic herd theory of long-range signaling in baleen whales. On the other hand, the synchrony might emerge when animals experience similar ecological conditions, which are, however, difficult to name because targeted depths and locations were separated for hundreds of meters and tens of kilometers, respectively. In this paper, we identify a framework for studying the sociality and behavior of such chaotically moving, unrestrained marine animals and call for more simultaneous tagging campaigns. Published by the American Physical Society 2024

Distance synchrony in coupled systems

We investigate the phenomenon of distance synchrony in a system of coupled conservative axially symmetric chaotic oscillators using master–slave type coupling. Our study reveals that the variables of the coupled oscillators achieve synchronization at a constant difference that depends on the coupling strength. This distance synchrony is explored and confirmed with two coupled as well as different types of network topologies. Our findings provide insight into the dynamics of coupled chaotic systems and contribute to the understanding of synchronization patterns in axially symmetric chaotic systems. We also provide analytical support for the numerical findings, along with achieving the same with experiments. This research has potential applications in various fields, including secure communications, neural networks, and other complex systems exhibiting chaotic behavior.