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Our aim is to study the Hopf bifurcation and synchronisation of a fractional-order butterfly-fish chaotic system. First, we derived the existence of a chaotic attractor in the fractional-order system and also synchronisation problem between two identical fractional-order chaotic systems is studied. Also, control design for the synchronisation with a suitable linear controller is tested in the response system. Finally, numerical simulation results are provided to confirm the theoretical analysis. [ABSTRACT FROM AUTHOR]

Nowadays various chaotic secure communication systems based on synchronization of chaotic circuits are widely studied. To achieve synchronization, the control signal proportional to the difference between the circuits signals, adjust the state of one circuit. In this paper the synchronization of two Chua circuits is simulated in Simulation Programs with Integrated Circuit Emphasis. It is shown that the choice of control signal is not straightforward, especially in the case of multistability and hidden attractors. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive finite-time modified function projective lag synchronisation with definite attenuation rate for a class of chaotic systems with unknown parameters. Firstly, a novel integral type terminal sliding surface is proposed to ensure the finite-time stability of the sliding motion. Subsequently, an adaptive finite-time control law is designed to guarantee the occurrence of the sliding motion in a limited time and the accurate estimation of the unknown parameters. Moreover, the exponential attenuation rate designed in this paper can further cut down the synchronisation time. Numerical simulations are presented to verify the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper investigates the observer design problem for 1D wave equation with nonlinear boundary condition containing a forcing term, whose dynamics presents spatiotemporal chaotic behaviors. By introducing a linear error input on the left-end boundary, we construct an observer via themethod of characteristics. Moreover, we present a sufficient and necessary condition for the stability of the error dynamics system. Numerical simulations are presented to illustrate the theoretical outcomes. [ABSTRACT FROM AUTHOR]

The following article serves three purposes: (i) it presents a simple semi-implicit numerical formulation for nonlinear structural dynamics problems, which is computationally inexpensive and simple to use in nonlinear dynamics and chaos simulations; (ii) it serves as an introduction to numerical studies of nonlinear structural dynamics for engineering students; and (iii) it formulates a nonlinear structural dynamical system for studies of nonlinear dynamics and chaos. Numerical formulations along with results are presented for nonlinear oscillators, beams, Föppl–von Kármán plates, and thin shallow shells. [ABSTRACT FROM AUTHOR]

Synchronisation conditions are studied for composite chaotic systems with complex compound structure and the signum function based on the theorem of zero-solution stability for a class of linear time-varying systems with countable discontinuous points. The synchronisation controller and its gain range are deduced according to the stability theorem, where the gain of the controller can speed synchronisation. Numerical simulation further proves the control theory and the validity of the synchronisation controller. The proposed controller can be widely applied in those chaotic systems with switch functions or other hybrid chaotic systems. [ABSTRACT FROM PUBLISHER]

In this study, numerical calculations using single- and two-phase models of CuO/water nanofluid forced convection in a three-dimensional C-shaped channel with constant heat flux are investigated. The laminar heat transfer enhancement using a nanofluid in a chaotic flow is first validated with the available data in the literature and the maximum discrepancy is within 3%; then further it is extended to design the C-shaped geometry. In addition, after comparisons of the numerical results with single- and two-phase models, the multiparameter constrained the optimization procedure integrating the design of experiments (DOE), response surface methodology (RSM), genetic algorithm (GA), and computational fluid dynamics (CFD) is proposed to design the nanofluid laminar convection of three-dimensional C-shaped channels. The thermal performance factors predicted by the regression function for the C-shaped channel case are in good agreement with the numerical results of CFD, with the difference being within 10%. [ABSTRACT FROM AUTHOR]

This article studies the linear quadratic regulator (LQR)-based optimal control law for chaotic dynamical system. First, we show a systematic and effective framework for modelling of chaotic system by considering the dynamics of bouncing ball on sinusoidally oscillating surface and explore the similarity between dynamics of the standard chaotic map and bouncing ball dynamics. Then we investigated the discrete LQR optimal control technique to the control of chaotic system. The investigated design method is conceptually simple and computationally efficient. The effectiveness of the design method is demonstrated by simulation results. [ABSTRACT FROM PUBLISHER]

Fractional order dynamics and chaotics systems have been recently combined, yielding interesting behaviours. In this paper, a novel integer order hyperchaotic system is considered. Then, a fractional order hyperchaotic representation of said system is proposed using a natural fractionalization. Two different linear control methodologies to deal with the complexity which introduce such systems are proposed. Those methods are able to modify the hyperchaotic behaviour of the system and force it to move towards a fixed point; i.e. steady state. These approaches give a general framework for taming such complex systems using simple linear controllers. The main tools for analysing the controlled system are Matignon stability criterion and RouthHurwitz test. Using a reliable numerical simulation, the designed system is simulated to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

An evolutionary image-detection method based on a novel chaotic hybrid optimizing algorithm (CHOA) is proposed. The method combines the strengths of particle swarm optimization (PSO), genetic algorithms (GAs), and chaotic dynamics (CD), and involves the standard velocity and position update rules of PSOs with the ideas of selection, crossover, and mutation from GA. In addition, the notion of species is introduced into the proposed CHOA to enhance its performance in solving multimodal problems. The effectiveness of the species-based chaotic hybrid optimizing algorithm (SCHOA) is proven through simulations and benchmarking, and finally, it is successfully applied to solve a multitemplate matching (MTM) problem in the printed circuit board (PCB) industry, as well as circle-detection problems. To make it more powerful in solving circle-detection problems in complicated circumstances, the notion of “tolerant radius” is proposed and incorporated into the SCHOA method. Simulation tests were undertaken on several hand-drawn sketches and natural photos, and the effectiveness of the proposed method was clearly shown through the test results. [ABSTRACT FROM AUTHOR]

In this paper, a new 3D autonomous Lorenz-type chaotic system is modelled based on the condition that the system may generate chaos whereas it has only stable or non-hyperbolic equilibrium points. This system also includes some well-known Lorenz-like systems as its special cases, such as the diffusionless Lorenz system, the Burke-Shaw system and some other systems found. Although the new chaotic system is similar to other Lorenz-type systems in algebraic structure, they are topologically non-equivalent. This interesting fact motivates one to further investigate its dynamical behaviours, such as the number and the stability of equilibrium points, Hopf bifurcation and its direction, Poincaré maps, Lyapunov exponents and dissipativity, etc. Given numerical simulations not only verify the corresponding theoretically analytical results, but also demonstrate that this system possesses abundant and complex dynamical properties, which need further attention. [ABSTRACT FROM AUTHOR]

This article reports a numerical study on the roads to chaos for a transient laminar natural convection in a square enclosure with horizontal adiabatic walls. The other walls, composed of two regions of the same size, were assumed isothermal. Transfer equations were solved using the vorticity-stream function formulation. The effects of Rayleigh number on heat transfer were also analyzed, and the roads to chaos borrowed by the convective flow. As the Rayleigh number increased, the flow structure started from four-cells to oscillatory three-cells. The first Hopf bifurcation was observed. Quasi-periodic flows appeared before the chaos onset. [ABSTRACT FROM AUTHOR]

In this article, a new type of multi-agent system model with mixed coupling topologies is proposed for realizing pattern formations with specific geometric shapes and formation splitting. The interactions among individual agents are assumed to be universally repulsive and selectively attractive. By designing the form of attractive coupling matrix, one can obtain a variety of formations with specific shapes in the system through self-assembly of agents. Both symmetric coupling case and asymmetric coupling case are considered. Analysis and simulation results show symmetric ones result in convergent dynamics to steady-state formations, whereas, for asymmetric case, the system exhibits complex dynamic behaviours, including collective rotation and chaotic motion. By breaking the graph defined by attractive couplings into disjoint subgraphs, one can make the formation of agents to split into small sizes. The results are relevant for the design of coordination and cooperative control for multi-agent systems. [ABSTRACT FROM AUTHOR]

The Session Initiation Protocol (SIP) retransmission mechanism can cause SIP network collapse with short-term overload. In this paper, we investigate with a fluid modelling approach the chaotic behaviour of the SIP retransmission mechanism in SIP networks. We capture the complex correlation structure in SIP systems through a detailed and novel queuing analysis. To dimension a buffer size which can avoid unnecessary message drop in a SIP server, we develop a sufficient condition for a stable SIP system analytically based on our fluid model. We also apply our fluid model to the simulation of a complex SIP system. We compare the simulation results achieved through our fluid models with those based on OPNET®event-driven approach to demonstrate the validity of our approach. [ABSTRACT FROM AUTHOR]

In this article, we propose a chaotic interleaving scheme for continuous-phase modulation-based orthogonal frequency-division multiplexing (CPM-OFDM) systems. The idea of chaotic maps randomisation (CMR) is exploited in this scheme. CMR generates permuted sequences from the sequences to be transmitted with lower correlation among their samples, and hence a better Bit Error Rate (BER) performance can be achieved. The proposed CMR-CPM-OFDM system combines the advantages of frequency diversity and power efficiency from CPM-OFDM and performance improvement from chaotic interleaving. The BER performance of the CPM-OFDM system with and without chaotic interleaving is evaluated by computer simulations. Also, a comparison between chaotic interleaving and block interleaving is performed. Simulation results show that, the proposed chaotic interleaving scheme can greatly improve the performance of CPM-OFDM systems. Furthermore, the results show that the proposed chaotic interleaving scheme outperforms the traditional block interleaving scheme for CPM-OFDM systems. The results show also that, the proposed CMR-CPM-OFDM system provides a good trade-off between system performance and bandwidth efficiency. [ABSTRACT FROM AUTHOR]

In this article, the author extends Dawid and Feichtinger's chaotic advertising diffusion model into the duopoly case. A computer simulation system is used to test this enhanced model. Based on the analysis of simulation results, it is found that the best advertising strategy in duopoly is to increase the advertising investment to reach the best Win–Win situation where the oscillation of market portion will not occur. In order to effectively arrive at the best situation, we define a synthetic index and two thresholds. An estimation method for the parameters of the index and thresholds is proposed in this research. We can reach the Win–Win situation by simply selecting the control parameters to make the synthetic index close to the threshold of min-oscillation state. The numerical example and computational results indicated that the proposed chaotic model is useful to describe and analyse advertising diffusion process in duopoly, it is an efficient tool for the selection and optimisation of advertising strategy. [ABSTRACT FROM AUTHOR]

A discrete nonlinear dynamics model has been established based on investment competition for heterogeneous financial institutions in this paper. The cost functions of financial institutions are different in the competitive investment. Theoretical analysis and numerical simulations of the system are investigated in detail. The results show that the dynamic system can undergo chaotic orbits. The stability control is realized by the method combining the feedback control with the parameter variation. The numerical simulation results show that the control method is effective. In practice, by utilizing the sensitivity to disturbance of the model, we can put a tiny perturbation on the chaotic system and induce large influence on investments in order to realize a desirable behaviour. [ABSTRACT FROM PUBLISHER]

Phase transitions in spin-glass type systems and, more recently, in related computational problems have gained broad interest in disparate arenas. In the current work, we focus on the “community detection” problem when cast in terms of a general Potts spin-glass type problem. As such, our results apply to rather broad Potts spin-glass type systems. Community detection describes the general problem of partitioning a complex system involving many elements into optimally decoupled “communities” of such elements. We report on phase transitions between solvable and unsolvable regimes. A solvable region may further split into “easy” and “hard” phases. Spin-glass type phase transitions appear at both low and high temperatures (or noise). Low-temperature transitions correspond to an “order by disorder” type effect wherein fluctuations render the system ordered or solvable. Separate transitions appear at higher temperatures into a disordered (or an unsolvable) phase. Different sorts of randomness lead to disparate behaviors. We illustrate the spin glass character of both transitions and report on memory effects. We further relate Potts type spin systems to mechanical analogs and suggest how chaotic-type behavior in general thermodynamic systems can indeed naturally arise in hard computational problems and spin glasses. The correspondence between the two types of transitions (spin glass and dynamic) is likely to extend across a larger spectrum of spin-glass type systems and hard computational problems. We briefly discuss potential implications of these transitions in complex many-body physical systems. [ABSTRACT FROM PUBLISHER]

Chaos control and synchronization problem of a three-species food chain model with Holling I-type functional response is investigated. By the linearization approach, a feedback control law is developed to stabilize the model system to equilibrium points. Based on the bidirectional coupled method, chaos synchronization of the model system is studied. Numerical simulations show that the feedback control law can suppress chaos to unstable equilibrium points successfully. Further, the numeric results show that when the coupling strength 0

In this work we study CO oxidation by numerical simulation; we used the monocrystal STM model (Sales et al., 1982; Slinko et al., 1999) and extended it to scale on a monolithic tubular reactor. The final model is a mixed system with ordinary and partial differential equations. We found that there is periodic behavior at earlier times, but the simulations at long time show bursting, which appeared as a route to chaotic behavior. Our results can be compared indirectly with a continuous flow reactor under isothermal conditions (Ballandis and Plath, 2000). [ABSTRACT FROM AUTHOR]

A dynamic model of the inverted pendulum characteristics of the head and cervical spine is presented. Using simple approximations and a single rotational-degree-of-freedom approach, the model is shown to conform to the classical mathematical description of an inverted pendulum motion. It also exhibits the well-known point of unstable equilibrium which is a standard property of such systems. Specific predictions of this theoretical description are compared against other values for the tilt, angular velocity and acceleration of the head during acceleration-sled testing, and with the Kapitza relation for mechanical-dither stabilization of an inverted pendulum. Numerical evaluations of the dynamic variables, resonant frequencies and time constants important to the problem are provided, and suggestions are made about how further results might be derived from extended versions of the model. This approach can now be refined to serve as a testing ground for analysing the biomechanics of traumatic neck injuries and for interpreting the possible roles that mandibular dysfunctions and dental malocclusion may play in disorders of the cervical spine. (Some background needed for exploring the latter possibility is presented.) [ABSTRACT FROM AUTHOR]

The possibility of constructing chaotic and complex periodic orbits of desired configurations is demonstrated on one-dimensional discontinuous maps. With appropriately located discontinuity, these maps can generate a rich selection of specific orbits with long laminar segments. A simple method is proposed to determine the features of the orbit obtained. This technique, applied to special maps with a horizontal linear branch, allows us to generate a great variety of stable periodic orbits with a specified future by only small variations of the map control parameter. [ABSTRACT FROM AUTHOR]