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This work proposes a family of modulo-based one-dimensional maps with three control parameters. The input to the modulo function includes the addition of three terms, the map's previous value, a scalar, and a multiple of a chosen seed function. Under certain conditions, the proposed maps will have no equilibria, which brings them into the category of maps with hidden attractors. Moreover, the maps can showcase wide parametric regions of uninterrupted chaotic behavior, indicative of robust chaos. The above properties are studied for a collection of different seed functions, inspired by well-known chaotic maps. The results are demonstrated by a series of numerical tools, like phase diagrams, bifurcation diagrams, Lyapunov exponent diagrams, and the 0–1 test. Finally, the maps are successfully applied to the design of a pseudo-random bit generator. [ABSTRACT FROM AUTHOR]

This paper presents a new method of generating chaotic maps that do not have fixed points. The method uses an appropriate transformation of functions defined on the unit square in such a way that the newly created projection has no fixed points. In this way, countless new chaotic mappings can be created, both piecewise linear and nonlinear, that belong to the family of systems with hidden attractors. The new family of maps is presented in three examples showing phase diagrams, bifurcation diagrams, and space parameters of the Lyapunov exponent. The discussed examples of mappings were created by appropriate logistic and tent mapping transformations, and their combination. In addition, this paper analyzes the applications of the new families of chaotic mappings in chaotic cryptography. Furthermore, an algorithm for generating pseudorandom bit values (PRBG) is also presented based on the examples of proposed mappings. [ABSTRACT FROM AUTHOR]

In this work, a family of piecewise chaotic maps is proposed. This family of maps is parameterized by the nonlinear functions used for each piece of the mapping, which can be either symmetric or non-symmetric. Applying a constraint on the shape of each piece, the generated maps have no equilibria and can showcase chaotic behavior. This family thus belongs to the category of systems with hidden attractors. Numerous examples of chaotic maps are provided, showcasing fractal-like, symmetrical patterns at the interchange between chaotic and non-chaotic behavior. Moreover, the application of the proposed maps to a pseudorandom bit generator is successfully performed. [ABSTRACT FROM AUTHOR]

This article is involved in chaos criteria and chaotification schemes on one kind of first-order partial difference equations having non-periodic boundary conditions. Firstly, four chaos criteria are achieved by constructing heteroclinic cycles connecting repellers or snap-back repellers. Secondly, three chaotification schemes are obtained by using these two kinds of repellers. For illustrating the usefulness of these theoretical results, four simulation examples are presented.

Many drawbacks in chaos-based applications emerge from the chaotic maps' poor dynamic properties. To address this problem, in this paper a chaotification model based on modulo operator and secant functions to augment the dynamic properties of existing chaotic maps is proposed. It is demonstrated that by selecting appropriate parameters, the resulting map can achieve a higher Lyapunov exponent than its seed map. This chaotification method is applied to several well-known maps from the literature, and it produces increased chaotic behavior in all cases, as evidenced by their bifurcation and Lyapunov exponent diagrams. Furthermore, to illustrate that the proposed chaotification model can be considered in chaos-based encryption and related applications, a voice signal encryption process is considered, and different tests are being used with respect to attacks, like brute force, entropy, correlation, and histogram analysis.

Many shortcomings of chaos-based applications stem from the weak dynamic properties of the chaotic maps they use. To alleviate this problem, inspired by the buffeting effect in aeroelasticity, this article proposes the buffeting chaotification model (BCM). Using the especially designed buffeting and modulo operators, the BCM can generate numerous new chaotic maps with strong dynamic properties from existing one-dimensional chaotic maps. The effectiveness of the BCM is mathematically proven according to the Lyapunov exponent, and further numerical experiments confirm the superiority of the chaotic maps generated by the BCM in terms of the dynamic properties. The field-programmable gate array implementation also shows that the BCM owns simplicity in hardware devices. To investigate the practical application, a scheme for constructing the pseudorandom number generator is designed. Performance analyses indicate that our generators have a strong ability to produce high-quality pseudorandom sequences rapidly. [ABSTRACT FROM AUTHOR]

In this work, we consider polynomial approximations of the sine map, which is known to be chaotic. The dynamics of the maps obtained for different orders of approximations are studied using classical tools. Comparison of the behavior is made through common bifurcation diagrams, 0–1 test results, Lyapunov exponent diagrams and approximate entropy diagrams. Furthermore, the differences between the Lyapunov exponents and approximate entropy are depicted, to provide a better grasp on the comparison. It is demonstrated that different orders of approximations lead to the definition of distinct chaotic systems, which in cases attain more complex chaotic behavior compared to the original sine map. Furthermore, the basins of stability for the proposed maps are thoroughly studied. Subsequently, considering the fact that the sine map is commonly utilized in the definition of more complex maps, the effects of substituting the sine map with its approximates is investigated. It is shown that in many occasions the dynamics of the map defined using the Taylor approximation is more complex compared to the original map. Finally, two of the proposed maps are used for the definition of two pseudorandom bit generators, whose randomness is verified via statistical tests. [ABSTRACT FROM AUTHOR]

In this work, a family of piecewise chaotic maps is proposed. This family of maps is parameterized by the nonlinear functions used for each piece of the mapping, which can be either symmetric or non-symmetric. Applying a constraint on the shape of each piece, the generated maps have no equilibria and can showcase chaotic behavior. This family thus belongs to the category of systems with hidden attractors. Numerous examples of chaotic maps are provided, showcasing fractal-like, symmetrical patterns at the interchange between chaotic and non-chaotic behavior. Moreover, the application of the proposed maps to a pseudorandom bit generator is successfully performed.

In this work, a chaotification technique is proposed that can be used to enhance the complexity of any one-dimensional map by adding the remainder operator to it. It is shown that by an appropriate parameter choice, the resulting map can achieve a higher Lyapunov exponent compared to its seed map, and all periodic orbits of any period will be unstable, leading to robust chaos. The technique is tested on several maps from the literature, yielding increased chaotic behavior in all cases, as indicated by comparison of the bifurcation and Lyapunov exponent diagrams of the original and resulting maps. Moreover, the effect of the proposed technique in the problem of pseudo-random bit generation is studied. Using a standard bit generation technique, it is shown that the proposed maps demonstrate increased statistical randomness compared to their seed ones, when used as a source for the bit generator. This study illustrates that the proposed method is an efficient chaotification technique for maps that can be used in chaos-based encryption and other relevant applications. [ABSTRACT FROM AUTHOR]

This paper studies chaos and chaotification for a class of first-order partial difference equations with a finite or infinite system size by using the theory of heteroclinic cycles connecting repellers. Three criteria of chaos induced by regular and nondegenerate heteroclinic cycles connecting repellers or regular heteroclinic cycles connecting repellers are established, respectively. Especially, one chaotification theorem for general discrete systems in the finite-dimensional space Y k or the infinite-dimensional space l ∞ is established, which is also based on heteroclinic cycles connecting repellers. Then, by using this result, two chaotification schemes for first-order partial difference equations are established. For illustrating the existence of chaos and the validity of chaotification schemes, three examples are provided with computer simulations. [ABSTRACT FROM AUTHOR]

Chaotic maps with higher chaotic complexity are urgently needed in many application scenarios. This paper proposes a chaotification model based on sine and cosecant functions (CMSC) to improve the dynamic properties of existing chaotic maps. CMSC can generate a new map with higher chaotic complexity by using the existing one-dimensional (1D) chaotic map as a seed map. To discuss the performance of CMSC, the chaos properties of CMSC are analyzed based on the mathematical definition of the Lyapunov exponent (LE). Then, three new maps are generated by applying three classical 1D chaotic maps to CMSC respectively, and the dynamic behaviors of the new maps are analyzed in terms of fixed point, bifurcation diagram, sample entropy (SE), etc. The results of the analysis demonstrate that the new maps have a larger chaotic region and excellent chaotic characteristics. [ABSTRACT FROM AUTHOR]

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.

Motivated by the concept of cascade operator and sine enhanced model, this paper proposes a universal framework termed cascade-sine chaotification model (CSCM) for producing chaotic maps. The principle of the proposed method is to perform sine transformation on the outputs of the seed maps, and then cascade the results to construct new systems. Compared with one-dimensional (1D) nonlinear models, the CSCM can produce diverse chaotic maps with arbitrary dimensionality by combining existing seed maps. Moreover, the chaotic maps generated by CSCM possess extremely higher complexity and larger chaotic ranges than the seed maps. To verify the effectiveness of CSCM, four chaotic maps generated by CSCM are presented as examples, of which the dynamical properties are systematically analyzed. Simulation results indicate the generated systems perform robust hyperchaotic properties in a large parameter range. Finally, a pseudo-random number generator (PRNG) is introduced to investigate the practicability of CSCM and the test results demonstrate the randomness of the obtained chaotic sequences. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive fuzzy generalized predictive controller is proposed for the anti-chaos control where the system dynamics are assumed to be unknown or uncertain in large. In the proposed mechanism, the control signal is generated by an input constraint generalized predictive controller to track the Duffing oscillator which is used as a chaotic reference system. The adaptive fuzzy system, as a real plant model, is employed to obtain prediction through the receding horizon. In order to show the capability of the proposed mechanism, three different payloads and noise cases are studied in the real-time control experiments of flexible-joint manipulator and tracking results are compared with three more non-model-based controllers which are conventional adaptive fuzzy control, indirect adaptive fuzzy sliding mode controller and proportional–integrative–derivative control. Results show that the proposed mechanism has better control performance than the others. [ABSTRACT FROM AUTHOR]

In this work, a chaotification technique is proposed that can be used to enhance the complexity of any one-dimensional map by adding the remainder operator to it. It is shown that by an appropriate parameter choice, the resulting map can achieve a higher Lyapunov exponent compared to its seed map, and all periodic orbits of any period will be unstable, leading to robust chaos. The technique is tested on several maps from the literature, yielding increased chaotic behavior in all cases, as indicated by comparison of the bifurcation and Lyapunov exponent diagrams of the original and resulting maps. Moreover, the effect of the proposed technique in the problem of pseudo-random bit generation is studied. Using a standard bit generation technique, it is shown that the proposed maps demonstrate increased statistical randomness compared to their seed ones, when used as a source for the bit generator. This study illustrates that the proposed method is an efficient chaotification technique for maps that can be used in chaos-based encryption and other relevant applications.

In this work, we demonstrate numerically that two-frequency excitation is an effective method to produce chaotification over very large regions of the parameter space for the Duffing oscillator with single- and double-well potentials. It is also shown that chaos is robust in the last case. Robust chaos is characterized by the existence of a single chaotic attractor which is not altered by changes in the system parameters. It is generally required for practical applications of chaos to prevent the effects of fabrication tolerances, external influences, and aging that can destroy chaos. After showing that very large and continuous regions in the parameter space develop a chaotic dynamics under two-frequency excitation for the double-well Duffing oscillator, we demonstrate that chaos is robust over these regions. The proof is based upon the observation of the monotonic changes in the statistical properties of the chaotic attractor when the system parameters are varied and by its uniqueness, demonstrated by changing the initial conditions. The effects of a second frequency in the single-well Duffing oscillator is also investigated. While a quite significant chaotification is observed, chaos is generally not robust in this case. [ABSTRACT FROM AUTHOR]

This paper is mainly devoted to the investigation of discrete-time fractional systems in three aspects. Firstly, the fractional Bogdanov map with memory effect in Riemann–Liouville sense is obtained. Then, via constructing suitable controllers, the fractional Bogdanov map is shown to undergo a transition from regular state to chaotic one. Meanwhile, the positive largest Lyapunov exponent is calculated by the Jacobian matrix algorithm to distinguish the chaotic areas. Finally, the Grassberger–Procaccia algorithm is employed to evaluate the correlation dimension of the controlled fractional Bogdanov system under different parameters. The main results show that the correlation dimension converges to a fixed value as the embedding dimension increases for the controlled fractional Bogdanov map in chaotic state, which also coincides with the conclusion driven by the largest Lyapunov exponent. Moreover, three-dimensional fractional Stefanski map is considered to further verify the effectiveness and generality of the obtained results. [ABSTRACT FROM AUTHOR]

Chaotic systems are widely employed in many practical applications for their significant properties. Existing chaotic systems may suffer from the drawbacks of discontinuous chaotic ranges and frail chaotic behaviors. To solve this issue, this paper proposes a two-dimensional (2D) sine chaotification system (2D-SCS). 2D-SCS can not only significantly enhance the complexity of 2D chaotic maps, but also greatly extend their chaotic ranges. As examples, this paper applies 2D-SCS to two existing 2D chaotic maps to obtain two enhanced chaotic maps. Performance evaluations show that these two enhanced chaotic maps have robust chaotic behaviors in much larger chaotic ranges than existing 2D chaotic maps. A microcontroller-based experiment platform is also designed to implement these enhanced chaotic maps in hardware devices. Furthermore, to investigate the application of 2D-SCS, these two enhanced chaotic maps are applied to design a pseudorandom number generator. Experiment results show that these enhanced chaotic maps can produce better random sequences than the existing 2D and several state-of-the-art one-dimensional (1D) chaotic maps. [ABSTRACT FROM AUTHOR]

Over the last 40 years, the design of n -dimensional hyperchaotic systems with a maximum number (n − 2) of positive Lyapunov exponents has been an open problem for research. Nowadays it is not difficult to design n -dimensional hyperchaotic systems with less than (n − 2) positive Lyapunov exponents, but it is still extremely difficult to design an n -dimensional hyperchaotic system with the maximum number (n − 2) of positive Lyapunov exponents. This paper aims to resolve this challenging problem by developing a chaotification approach using average eigenvalue criteria. The approach consists of four steps: (i) a globally bounded controlled system is designed based on an asymptotically stable nominal system with a uniformly bounded controller; (ii) a closed-loop pole assignment technique is utilized to ensure that the numbers of eigenvalues with positive real parts of the controlled system be equal to (n − 1) and (n − 2), respectively, at two saddle-focus equilibrium points; (iii) the number of average eigenvalues with positive real parts is ensured to be equal to (n − 2) for the controlled system over a given control period; (iv) the smallest value of the positive real parts of the average eigenvalues is ensured to be greater than a given threshold value. Finally, the paper is closed with some typical examples which illustrate the feasibility and performance of the proposed design methodology. [ABSTRACT FROM AUTHOR]

This paper focuses on chaotification problems for first-order partial difference equations. Two chaotification schemes of the difference equations via sine functions are established, and all the controlled systems are proved to be chaotic in the sense of both Devaney and Li-Yorke by applying the coupled-expansion theory of general discrete dynamical systems. At the end, one illustrative example is provided. [ABSTRACT FROM AUTHOR]

We present in this paper, two new chaotification methods: The first is about chaotifying one-dimensional discrete mappings using the notion of S -unimodality and the second one is about chaotifying one-dimensional discrete mappings using Collet–Eckmann condition. These two methods are valid only for one-dimensional discrete mappings. [ABSTRACT FROM AUTHOR]

Chaotification, aiming to make an original nonchaotic system chaotic, or enhancing an existing chaos, has attracted much attention recently. This paper investigates chaotification problem of stable linear complex networks, both discrete and continuous systems, via single pinning impulsive control. Under this scheme, the boundedness of these linear networks can be guaranteed, and the largest Lyapunov exponent of these controlled linear complex networks can be calculated in detail by theoretical analysis. Finally, two numerical examples are given to demonstrate the effectiveness of this strategy. [ABSTRACT FROM AUTHOR]

When chaotic systems are used in different practical applications, such as nonlinear control and cryptography, their complex chaos dynamics are strongly required. However, many existing chaotic systems have simple complexity, and this brings negative effects to chaos-based applications. To address this issue, this paper introduces a sine chaotification model (SCM) as a general framework to enhance the chaos complexity of existing one-dimensional (1-D) chaotic maps. The SCM uses a sine function as a nonlinear chaotification transform and applies it to the output of a 1-D chaotic map. The resulting enhanced chaotic map of the SCM has better chaos complexity and a much larger chaotic range than the seed map. Theoretical analysis verifies the efficiency of the SCM. To show the performance of the SCM, we apply SCM to three existing chaotic maps and analyze the dynamics properties of the obtained enhanced chaotic maps. Performance evaluations prove that the three enhanced chaotic maps have more complicated dynamics behaviors than their seed chaotic maps. To show the implementation simplicity of the SCM, we implement the three enhanced chaotic maps using the field-programmable gate array. To investigate the SCM in practical application, we design pseudorandom number generators using the enhanced chaotic maps. [ABSTRACT FROM AUTHOR]

Little seems to be known about the chaotification control of fractional order linear and nonlinear systems. This paper proposes a novel chaotification method for fractional order nonlinear systems based on the negative damping instability mechanism and fractional calculus technique. We then apply it to chaotify the fractional order Lorenz system with order lying in ( 1 , 2 ) , which is stable originally with specific parameters. Moreover, we introduce three critical effective orders to distinguish different four dynamics: singleton sets attractor, self-excited attractor, coexisting attractors, and blow up behavior. Many simulations are carried out to illustrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

Generating chaotic maps with expected dynamics of users is a challenging topic. Utilizing the inherent relation between the Lyapunov exponents (LEs) of the Cat map and its associated Cat matrix, this paper proposes a simple but efficient method to construct an n -dimensional ( n -D) hyperchaotic Cat map (HCM) with any desired number of positive LEs. The method first generates two basic n -D Cat matrices iteratively and then constructs the final n -D Cat matrix by performing similarity transformation on one basic n -D Cat matrix by the other. Given any number of positive LEs, it can generate an n -D HCM with desired hyperchaotic complexity. Two illustrative examples of n -D HCMs were constructed to show the effectiveness of the proposed method, and to verify the inherent relation between the LEs and Cat matrix. Theoretical analysis proves that the parameter space of the generated HCM is very large. Performance evaluations show that, compared with existing methods, the proposed method can construct n -D HCMs with lower computation complexity and their outputs demonstrate strong randomness and complex ergodicity. [ABSTRACT FROM PUBLISHER]

Little seems to be known about the chaotification problem in the framework of fractional order nonlinear systems. Based on the negative damping instability mechanism and fractional calculus technique, this paper reports the onset of chaos in fractional order Lorenz system with periodic system parameters via asymptotically period-doubling cascade. To further understand the complex dynamics of the system, some basic properties such as the largest Lyapunov exponents, bifurcation diagram, routes to chaos, asymptotically periodic windows, possible chaotic and asymptotically periodic window parameter regions, and the compound structure of the system are analyzed and demonstrated with careful numerical simulations. Of particular interest is a striking finding that fractional derivative can chaotify the globally stable periodic system without feedback control. [ABSTRACT FROM AUTHOR]

Since the control energy for chaotification of Duffing-type dynamics system depends on the linear stiffness of the system, a quasi-zero-stiffness (QZS) isolated system with time delay control is introduced for line spectrum reconstruction of acoustic noise of machinery vibration of underwater vehicles. To investigate the critical condition for chaotification, the stability analysis of the dynamic system with time delay is conducted by the generalized Sturm criterion, and the analytical expression for critical control parameters is obtained. By converting the time-delayed differential equations of the critical condition into discrete mappings through a finite difference scheme, the Lyapunov criterion for chaotification of the QZS system is acquired, which yields the same critical time delay control as the results obtained by the generalized Sturm criterion. Effective chaotification by setting control parameters in the unstable region is demonstrated by numerical examples, which proves the accurate guidance of the stability analysis on chaotification design. [ABSTRACT FROM AUTHOR]

This paper focuses on the control problem of nonlinear discrete systems. An immersion and invariance (I&I) based approach is introduced to stabilize nonlinear discrete systems, and then extended to chaotify nonlinear discrete systems. Its basic idea is to immerse a reduced order system (target system) which holds prespecified properties into the plant system and then to control the trajectories of the plant system to converge towards the invariant manifold where the target system is immersed. For a class of nonlinear cascaded discrete systems, we find that there exist corresponding one-dimensional systems such that these systems can be chaotified and stabilized through I&I design. An illustrating example with simulation results is presented to validate the proposed chaotification and stabilization algorithms. [ABSTRACT FROM AUTHOR]

Over the last two decades, chaotification has received increasing attention from various communities of science and engineering. This paper aims at developing a unified chaotification framework for generating desired higher-dimensional dissipative hyperchaotic systems by using a single-parameter controller. The main idea is to use a block diagonal matrix in the design of the nominal system, so as to construct a desired hyperchaotic system. Specifically, the proposed scheme is to assign desired closed-loop poles to the controlled system, allocating the corresponding numbers of eigenvalues with positive real parts at two types of saddle-focus equilibria. For the non-degenerate case, the number of positive Lyapunov exponents of the controlled system is given by the largest number of positive Lyapunov exponents of the desired hyperchaotic system. Two representative examples are given to illustrate and verify the proposed design method. Finally, the digital signal processor is employed to implement the above 10-dimensional hyperchaotic systems, and the experimental observation is also given. [ABSTRACT FROM AUTHOR]

A method is proposed to chaotify a class of complex networks via impulsive control, when the orbits of the impulsive systems are confined in a bounded area. Based on computing the largest Lyapunov exponent, theoretical results and algorithmic analysis are given in details. Finally, numerical simulations are presented to illustrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]

This article is involved in chaos criteria and chaotification schemes on one kind of first-order partial difference equations having non-periodic boundary conditions. Firstly, four chaos criteria are achieved by constructing heteroclinic cycles connecting repellers or snap-back repellers. Secondly, three chaotification schemes are obtained by using these two kinds of repellers. For illustrating the usefulness of these theoretical results, four simulation examples are presented.

In this paper, a class of switching control systems is investigated, and a novel switching control method is developed, which can be applied to generating chaos dynamics from switching control systems through dwell time restriction. A numerical example is given to illustrate the generated chaotic dynamic behavior of the systems, and the corresponding bifurcation diagram is sketched. Then, the validity of the main results is verified together with other phase portraits. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of finite-time synchronization of jerk chaotic systems through a simple linear feedback control. The controller is designed such that practical finite-time synchronization could be achieved. As example, we use a new jerk system obtained thanks to the chaotification of the Duffing system using jerk architecture and simplification via a single silicon p-n junction diode. Mathematic proof, numerical and PSpice simulations, and practical results are presented to show the feasibility of the proposed scheme. The proposed method could be applied to all jerk-like systems. [ABSTRACT FROM AUTHOR]

This paper investigates a class of linear continuous-time switching systems and proposes a new approach to generate chaos by designing a hybrid switching rule. First, a computational formula for Lyapunov exponents is derived by extending the definition of Lyapunov exponent for continuous-time autonomous systems to that of a class of linear continuous-time switching systems. Then, a novel switching rule is proposed to gain global boundedness property as well as the required placement of Lyapunov exponents for chaos. A numerical example is given to illustrate the chaotic dynamic behavior of the generated system. The Lyapunov dimension of the system in the example is calculated and the corresponding bifurcation diagram and Lyapunov spectra are sketched, which, together with other phase portraits, clearly verify the validity of the main result. [ABSTRACT FROM AUTHOR]

This paper shows that two or more switched linear systems can generate chaotic dynamical behaviors by an appropriate switching rule as they at least consist of a controllable system and an unstable system with the expanding property. According to the results in the reference (Xie, L. L., Zhou, Y., and Zhao, Y. Criterion of chaos for switched linear systems with antrollers. International Journal of Bifurcation and Chaos, 20(12), 4105–4109 (2010)), a nonlinear feedback gain is needed to generate chaotic dynamics. A linear feedback control is usually used to approximate the nonlinear one for simulation. In order to obtain the exact control, as a main result of this paper, the controller is constructed by Russell’s result, and a block diagram is included to interpret the realization of the controller. Numerical simulations are given to illustrate the generated chaotic dynamical behavior of the switched linear systems with some parameters and show the effects of the constructed controller. [ABSTRACT FROM AUTHOR]

This paper introduces chaotic reference model-based dynamical state feedback chaotification method which can be applied to any input-state linearizable (nonlinear) system including linear controllable ones as special cases. In the developed method, any chaotic system of arbitrary dimension can be used as the reference model with no need to transform it into a special form, so providing the advantage of exploiting the vast amount of information on chaotic systems and their implementations available in the literature. To demonstrate the potential effective applications of the method, a permanent magnet dc motor is chaotified by the proposed dynamical state feedback as matching the closed loop dynamics to the well-known Chua's chaotic circuit. Then, an impeller mounted on the chaotified dc motor is used for mixing a corn syrup added acid-base mixture. It is observed in a nonintrusive way that mixing actuated by the chaotified dc motor is more efficient than constant and also periodical motor speed cases for the consideration of neutralization time and power consumption together. [ABSTRACT FROM AUTHOR]

Line spectrum of noise radiated from machinery vibrations of underwater vehicles is one of the most harmful signals that expose the characteristics of vehicles and locations. In order to distort the features and restrain the intensity of the line spectra, we attempt to chaotify the vibration system by time delay control. To avoid blindly numerical testing of the control parameters, stability of a two-dimensional vibration isolation floating raft system with two time-delayed feedback control is studied in this paper, aiming to provide guidance for chaotification. The system with dual equal time delay is investigated by the generalized strum method and the polynomial eigenvalues are adopted to analyze the stability of the controlled vibration isolation system with two unequal time delays. The critical control gains and delays for stability switches are obtained. By adjusting the control parameters beyond stable region, it is feasible to chaotify the system. Numerical simulations are conducted to compare the effect of two time delay with different control parameters and different control scheme to complicate the vibration isolation system. [ABSTRACT FROM AUTHOR]

This paper presents a chaotification method based on direct time-delay feedback control for a quasi-zero-stiffness isolation system. An analytical function of time-delay feedback control is derived based on differential-geometry control theory. Furthermore, the feasibility and effectiveness of this method was verified by numerical simulations. Numerical simulations show that this method holds the favorable aspects including the advantage of using tiny control gain, the capability of chaotifying across a large range of parametric domain and the high feasibility of the control implement. [ABSTRACT FROM AUTHOR]

Chaotification of dynamical systems is a hot topic in the research field of chaos in recent years. Previous studies showed that (even linear) discrete or continuous dynamical systems can be chaotified by designing appropriate controllers. Here, we study chaotification of linear impulsive differential systems. First, we propose a framework for chaotification of general linear impulsive differential systems that can be transformed into discrete maps. Then, we give technical details for how to chaotify several typical linear impulsive differential systems that are actually canonical forms, including how to design appropriate quadratic impulsive controllers, how to find snapback repellers in the Marotto theorem, etc. As one of the main theoretical results, we rigorously prove the existence of chaos in all the considered impulsive systems. In addition, numerical examples are used to verify the theoretical prediction in each case. We are expecting that our proposed approach can have practical applications in the engineering field. [ABSTRACT FROM AUTHOR]

In this paper, the chaos method for reducing line spectra of the radiated noise of marine vessels is implemented with the application of a control scheme, that is, chaotifing the nonlinear vibration isolation system (VIS) with an external chaotic system, such as the Lorenz system families. The scheme is similar to generalized synchronization of chaos to a considerable degree. Moreover, an implicit performance-index function and optimization strategy are proposed to obtain the optimal control gain for generating chaos with the highest quality. Numerical simulations are carried out and the results confirm the validity and effectiveness of the methods. [ABSTRACT FROM PUBLISHER]