Chunbiao Li

Nanjing University of Information Science & Technology · School of Artificial Intelligence

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

Electrolysis is an important way to produce manganese metal, but the low current efficiency and random growth of dendrites have always been challenging problems for enterprises. The lack of understanding of the dynamic system during the electrolysis process is the main reason for the accurate control of the electrolysis process. Based on this consi...

A comprehensive review of symmetry and conditional symmetry is made from the core conception of symmetry and conditional symmetry. For a dynamical system, the structure of symmetry means its robustness against the polarity change of some of the system variables. Symmetric systems typically show symmetrical dynamics, and even when the symmetry is br...

When both an absolute value function and a cosine function are introduced for chaotic sequence generation, coexisting attractors with different polarities and locations could be extracted by the offset boosting of the initial condition, and thus a hyperchaotic map with distance-increasing coexisting attractors is constructed. It is found that this...

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

A comprehensive review on symmetry and conditional symmetry is made from the core conception of symmetry and conditional symmetry. For a dynamical system, the structure of symmetry means its robustness against the polarity change of some of the system variables. Symmetric systems typically show symmetrical dynamics and even when the symmetry is bro...

For the second order and nonlinearity with a meminductor, it can be embedded into a system for chaos producing. It is found that a mathematical meminductor can be introduced into a jerk system, which results in the same oscillation. And consequently, the system can be realized based on a new structure dominated by a meminductor. In this paper, a pa...

Free control of a chaotic signal means that its various aspects such as amplitude, frequency and offset can be freely controlled, which is of great value for the application of chaotic circuits. However, such a chaotic circuit typically contains many quadratic terms requiring multiplier-oriented operations, which posts a great challenge to the desi...

A compact switchable chaotic oscillator is proven with great benefit for chaos-based application. The multifarious chaotic signals with multiple amplitude and frequency can save the circuit modules for signal conditioning. By introducing more linear terms in those chaotic systems with amplitude/frequency control, a compact multi-output chaotic syst...

Electrolytic manganese dioxide (EMD) is the critical component of the cathode material in modern alkaline, lithium, and sodium batteries. Aimed at the remediation of EMD crystalline structures, this research explored the effect of external power-supplying models on EMD structure regulation. The chaos electro circuit was found to impact the characte...

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

The offset as the average value of a variable plays an important role in signal processing and system design. Offset boosting can be realized by a non-bifurcation parameter or an initial condition. In this work, symmetric coexisting attractors with opposite polarity and a 2D hyperchaotic map with multiple modes of offset boosting are proposed, wher...

For the wide frequency spectrum of chaotic signals, it is difficult to realize chaotic signal conditioning. Therefore, researchers turn to the exploration of chaotic systems with independent non-bifurcation control for easy chaos modification. In this paper, a system with only one non-quadratic term is modified for providing multiscale amplitude/fr...

A hyperchaotic map with various patterns of coexisting attractors is found by introducing trigonometric functions. The periodicity of trigonometric functions, as a key factor of coexisting attractors, brings various possibilities for attractor self-producing. By introducing orthorhombic feedback of sinusoidal and cosine functions, the newly constru...

Offset boosting and amplitude control of chaos play an important role in chaos-based engineering applications. In this work, a simple 4D chaotic oscillator is designed with three independent offset boosters that provide a single control, synchronous reverse control, and even differential control. Moreover, the offset level of the related variables...

A discrete memristor is introduced into the Rulkov neuron to mimic biological neuronal synapse and modify firing dynamics. In the memristive Rulkov neuron, chaotic firing with local amplitude control is obtained, where the range of chaotic bursting can be modified by two independent controllers. These two independent bifurcation parameters provide...

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

A new method of color image encryption is proposed in this paper, with the combination of a two-dimensional (2D) Henon-like chaotic map and compressed sensing for better performance. A sinusoidal function is introduced into the 2D Henon map for increasing randomness. Image encryption algorithm includes three procedures: compression of a color image...

The existence of homoclinic orbits is discussed analytically for a class of four-dimensional manifold piecewise linear systems with one switching manifold. An interesting phenomenon is found, that is, under the same parameter setting, homoclinic orbits and chaos appear simultaneously in the system. In addition, homoclinic chaos can be suppressed to...

Chaotic neuronal oscillation is fired up when a locally active memristor is introduced into the Rössler system. Such a memristive Rössler system has two independent parameters providing local amplitude control, one of which even adjusts the amplitude and frequency of variables in a specific intermittent mode. Different neuronal firing modes are mod...

The average value of a system variable determines the position of its attractor. When the offset parameters come together and get disappeared after an algebraic operation, the location of the attractor is then governed by an initial condition only. In this case, parameter-dominated offset control turns out to be the initial condition-defined coexis...

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

As the bounds of convergence time (CT) for fixed-time (FxT) stability have connections with some parameters of the system, the existing methods of FxT stability are still not really FxT. Therefore, this article studies FxT synchronization of complex networks (CNs) by proposing a new FxT stability theorem. First, the new FxT stability theorem is pro...

In this article, sinusoidal functions are introduced to a discrete map for hyperchaos generation and attractor self-reproduction. The constructed map shares a unique structure with controllable symmetry and conditional symmetry, which exhibits compound lattice dynamics, including 1-D and 2-D attractor growth. The direction of attractor growth can b...

A linear resistive capacitive inductive shunted model of a Josephson junction with a topologically nontrivial behavior is considered in this paper. We have considered a fractional order flux controlled memristor to effectively model the feedback flux effects across the Josephson junction (JJ). The mathematical model of the proposed JJ oscillator is...

The study of the collective behavior of oscillators has grabbed great attention in recent years. Among all dynamical systems, multi-stable systems have received particular attention. This paper considers a ring network of non-locally coupled VB5 chaotic systems exhibiting multistability with linear coupling. The collective patterns of the oscillato...

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

By the combined feedback of exponential, cubic and sinusoidal nonlinearity, a hyperchaotic map is constructed, which has the distinct features as providing two unipolar hyperchaotic sequences and large area of hyperchaotic orbit. A fast video encryption algorithm that adopted the permutation-diffusion-permutation strategy was developed consequently...

Memristor can be designed based on the topological structure of a dynamical system. Lorenz system provides such a structure for memristor building, in which one of the system variables can be regarded as the internal variable of the mathematical model. Based on the strong load capacity of AD633, two such capacitors are coupled directly to construct...

By introducing an absolute value function for polarity balance, a unique hyperchaotic map with complete control and conditional symmetry is designed. Firstly, coexisting conditional symmetric bifurcations and hyperchaotic phase trajectories are found in the map. Then, two independent parameters are proven to provide a direct knob for partial and to...

Initial condition-dominated offset boosting provides a special channel for coexisting orbits. Due to the nonlinearity and inherent periodicity, sinusoidal function is often introduced into a dynamical system for multistability design. Typically, the distance between two attractors or two petals of an attractor is fixed. Moreover, any chaotic signal...

The neuron models have been widely applied to neuromorphic computing systems and chaotic circuits. However, discrete neuron models and their application in image encryption have not gotten a lot of attention yet. This paper first presents a novel neuron model with significant chaotic characteristics, by coupling a memristor into the proposed neuron...

Based on the special structure of variable-boostable chaotic system VB24, a quadratic flux-controlled memristor is embedded for the construction of a 3D memristive chaotic system with conditional symmetry. Coexisting oscillations with conditional symmetry are confirmed systematically based on the bifurcation analysis and circuit verification. Two c...

When a locally active memristor is applied to the Hindmarsh–Rose neuron, complex neuromorphological dynamics can be observed. Local active memristor leads to neuromorphological oscillation giving various neuron spiking. The rotation control is applied to explore the chaotic bursting. It is found that the amplitude of the neuron bursting changes reg...

A hyperchaotic circuit power supply system for electrodeposition of manganese was designed and employed. It was found that under the action of hyperchaotic current, the anodic potential oscillation behavior was suppressed to a certain extent under the action of the hyperchaotic current. The average oscillation period was increased by 5.6 s and the...

Based on a variable-boostable chaotic system, a conservative chaotic system with controllable amplitude and offset is proposed. The system exhibits rich symmetrical dynamics under different parameters and initial conditions. More interestingly, a parameter of memristor poses a partial amplitude control to a system variable. Furthermore, the derived...

Chaos Theory and Applications (March 2022 - Volume 4 - Issue 1) https://dergipark.org.tr/en/pub/chaos/issue/63571 ----------- 1) Jun MA. "Chaos Theory and Applications：The Physical Evidence, Mechanism are Important in Chaotic Systems. " 2) Burak ARICIOĞLU, Sezgin KAÇAR. "Circuit Implementation and PRNG Applications of Time Delayed Lorenz System....

In this paper, a three-dimensional chaotic system with a line equilibrium is studied, in which a single nonbifurcation parameter is used to control the amplitude and frequency. A variety of chaotic signals can be modified using the amplitude-frequency control switch. e realization of circuit simulation based on multisim further verifies the theoret...

Recently, the image segmentation algorithm based on neural network has made great progress in the field of medical image segmentation, but it still faces many challenges such as the small set of training sample data, the lackness of background training data, weak network generalization ability, and poor network performance. To overcome the above di...

Based on the analysis of polarity balance and exhaustive computer searching, a series of symmetric chaotic flows is found for hosting conditional symmetry. Symmetric structure shapes the elegant symmetric phase trajectory, and conditional symmetry permits the convenience of embedding an extra set of coexisting symmetric attractors. Bifurcation anal...

In this letter, a compact memristor structure unit is applied for constructing the discrete chaotic system and, consequently, a memristor-type chaotic mapping is designed. Two independent system parameters are proven to be partial and total amplitude controllers. Meanwhile, the internal memristor parameter returns the map a typical bifurcation. Fin...

The structure of a dynamical system is the key factor for investigating its multi-stability. Generally, a system can be divided into two categories; that is, a symmetric one and an asymmetric one. A dynamical system X˙=F(X)=(f1(X),f2(X),...,fN(X))(X=(x1,x2,...,xN)T) is symmetric if there exists a variable substitution: u1=-x1,u2=-x2,...,uk=-xk,ui=x...

As we discussed in the above chapters, many dynamical systems can produce similar attractors, specifically some of which [1–10] share the same Lyapunov exponents.

Signum and absolute value functions show great potential in chaos generation. Aiming to design an easy-to-use non-smooth circuit component, a Triode-based Analog Gate (TAG) is designed, which consists of only one triode, two op-amps and four resistors for analog signal selection. By choosing external resistors and signals, TAG can be easily extende...

Thanks to their distinct synaptic plasticity and memory effects, memristors not only can mimic biological neuronal synapses but also can describe the influence of external electromagnetic radiation. This paper proposes a novel memristive autapse-coupled neuron model (MACNM) using a locally active memristor as an autapse and simultaneously introduci...

Initial condition-dominated offset boosting provides a special channel to arrange coexisting orbits. Due to the nonlinearity and inherent periodicity, sinusoidal function is often introduced into a dynamical system for multistability design. In this paper, an initial-controlled double-scroll hyperchaotic map is constructed based on two sine functio...

A simple variable-boostable system is selected as the structure for hosting an arbitrarily defined memristor for chaos producing. The derived three-dimensional (3-D) memristive chaotic system shows its distinct property of offset, amplitude and frequency control. Owing its merits any desired number of coexisting attractors are embedded by means of...

Previous studies have shown that cyclic neural networks which have no autoexcitation and are unidirectional can not generate chaos. Inspired by this finding, the present paper constructs a new memristive neural network composed of three nodes connected by the simplest circular loop, whose synaptic weights are replaced by hyperbolic memristors. The...

Two generalized flux-controlled memristors are applied for hyperchaos generation, and following a four-dimensional hyperchaotic oscillator is constructed. The applied two memristors share a common internal control variable. The new hyperchaotic oscillator exhibits complex dynamics including coexisting chaos and attractor merging. A single constant...

Chaos Theory and Applications (November 2021 - Volume 3 - Issue 2) https://dergipark.org.tr/en/pub/chaos/issue/58077

Typically, a chaotic system with quadratic terms is realized based on integral summation circuits, where however operational amplifiers and multipliers are usually overused. In this paper, a new approach for simplifying such circuit implementation is proposed utilizing the inherent characteristics of a multiplier. As a result, a chaotic system with...

In this paper, the current-controlled DC–DC buck converter from a new perspective are studied through the switching theory of flow, and the analytical conditions of the switching motion at the collision boundary and time boundary are both developed. Various mapping structures in periodic and chaotic status are visualized through phase trajectory an...

The special regime of multistability of attractor self-reproducing is deeply decoded based on the conception of offset boosting in this letter. Attractor self-reproducing is essentially originated from periodic initial condition-triggered offset boosting. Typically, a trigonometric function is applied for attractor self-reproducing. The position, s...

By introducing a discrete memristor and periodic sinusoidal functions, a two-dimensional map with coexisting chaos and hyperchaos is constructed. Various coexisting chaotic and hyperchaotic attractors under different Lyapunov exponents are firstly found in this discrete map, along with which other regimes of coexistence such as coexisting chaos, qu...

A variable boostable chaotic system and the Hindmarsh–Rose neuron model are applied for observing the dynamics revised by memristive computation. Nonlinearity hidden in a memristor makes a dynamic system prone to be chaos. Inherent dynamics in a dynamic system can be preserved in specific circumstances. Specifically, as an example, offset boosting...

Memristors are widely used to construct multi-scroll/wing chaotic systems with complex dynamics. However, the generation of a multi-scroll/wing attractor is typically not induced by the memristor but depends on other nonlinear functions in the system, which does not take advantage of the unique features of the memristor for chaos-based applications...

In this paper, through the discontinuous dynamical system theory, the system interactions of two distinct Van der Pol-Duffing oscillators and a Memristor-Duffing oscillator is discussed under a switching nonlinear controller with symbolic functions. The interaction conditions of three chaotic systems are treated as separation boundaries which is ti...

Manganese metal electrolysis is a typical nonlinear system far from the equilibrium state. In this case, nonlinear behaviors such as electrochemical oscillation and metal fractal occur in the electrode reaction process. The multiple valence state changes of manganese and the nonlinear coupling of multiple chemical reactions cause the electrolytic p...

Offset boosting is an important issue for chaos control due to its broadband property and polarity control. There are two main approaches to realize offset boosting. One is resort to parameter introducing where an offset booster realizes attractor boosting. The other one is by the means of periodic function or absolute value function where a specif...

Due to the natural nonlinearity and unique memory characteristics, memristors are promising candidates for the construction of multi-scroll attractors having better application potential in the field of information encryption than the traditional double-scroll attractors. This paper proposes a novel memristive multi-double-scroll Chua's system (MMD...

By introducing a sinusoidal function into a three-dimensional map, a hyperchaotic map with three positive Lyapunov exponents is derived. The map has two amplitude controllers, a total controller, and a partial controller. The hyperchaotic map shares a unique structure of two-leaf and three-leaf attractors under united Lyapunov exponents. Furthermor...

Chaos Theory and Applications (June 2021 - Volume 3 - Issue 1) https://dergipark.org.tr/tr/pub/chaos/issue/56378

A memristive chaotic system is proposed, which has the properties of conditional symmetry, attractor growing and amplitude frequency control. The introduced sinusoidal function wins its conditional symmetry giving coexisting chaotic attractors while the tangent function realizes attractor self-reproducing in other two dimensions. Due to the two per...

Little is known about bifurcations in two-dimensional (2D) differential systems from the viewpoint of Kosambi–Cartan–Chern (KCC) theory. Based on the KCC geometric invariants, three types of static bifurcations in 2D differential systems, i.e. saddle-node bifurcation, transcritical bifurcation, and pitchfork bifurcation, are discussed in this paper...

An absolute value function was introduced for chaos construction, where hyperchaotic oscillation was found with amplitude rescaling. The nonlinear absolute term brings the convenience for amplitude control. Two regimes of amplitude control including total and partial amplitude control are discussed, where the attractor can be rescaled separately by...

Trigonometric functions were used to construct a 2-D symmetrical hyperchaotic map with infinitely many attractors. The regime of multistability depends on the periodicity of the trigonometric function, which is closely related to the initial condition. For this trigonometric nonlinearity and the introduction of an offset controller, the initial con...

The coupling between neuronal oscillator plays a significant role in their network performance. When the coupling is asymmetric in an electrical synapse connection, the entire dynamical behaviour of the neuron model changes. Such asymmetric synapse coupling on neuron models exposed to magnetic flux induction will display more complex behaviours. He...

A new 4D memristive chaotic system with an infinite number of equilibria is proposed via exhaustive computer search. Interestingly, such a new memristive system has a plane of equilibria and two other lines of equilibria. Lyapunov exponent and bifurcation analysis show that this system has chaotic solutions with coexisting attractors. The basins of...

Equilibria are a class of attractors that host inherent stability in a dynamic system. Infinite number of equilibria and chaos sometimes coexist in a system with some connections. Hidden chaotic attractors exist independent of any equilibria rather than being excited by them. However, the equilibria can modify, distort, eliminate, or even instead c...

By introducing a sinusoidal function into a three-dimensional map, a hyperchaotic map with three positive Lyapunov exponents is derived. The system has two amplitude controllers, a total controller, and a partial controller. The hyperchaotic map shares a unique structure of two-leaf and three-leaf attractors under united Lyapunov exponents. Further...