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This paper is concerned with a reaction–diffusion–advection chemostat model with two species growing and competing for a single-limited resource. By taking the growth rates of the two species as variable parameters, we study the effect of growth rates on the dynamics of this system. It is found that there exist several critical curves, which may classify the dynamics of this system into three scenarios: (1) extinction of both species; (2) competitive exclusion; (3) coexistence. Moreover, we take numerical approaches to further understand the potential behaviors of the above critical curves and observe that the bistable phenomenon can occur, besides competitive exclusion and coexistence. To further study the effect of advection and diffusion on the dynamics of this system, we present the bifurcation diagrams of positive equilibrium solutions of the single species model and the two-species model with the advection rates and the diffusion rates increasing, respectively. These numerical results indicate that advection and diffusion play a key role in determining the dynamics of two species competing in a flow reactor. [ABSTRACT FROM AUTHOR]

This paper investigates the nonlinear dynamical behaviors of a time-delayed supercavitating vehicle system varying with the system parameters, and proposes control strategies to stabilize the trajectory. A simplified dynamical model of the supercavitating vehicle is firstly constructed and then analyzed on its local and global stability in terms of different parameter values and initial conditions. Due to the forces resulting from the fins and the afterbody plane causing one of the system parameters to become a piecewise constant function of position, the system is described as a linear switched one with time delay. Both theoretical analysis and numerical simulations are adopted to describe the system behaviors. Several special phenomena such as bifurcations, deviation behaviors and period-doubling processes emerging from the system for a given set of parameters are discussed in detail in this paper. Besides, the equilibrium and chaotic solutions are accurately located by plotting the Lyapunov exponent map. Chaotic attractors present different strange forms with the variation of the parameters. Finally, based on the system's global property, the control and anti-control strategies are proposed to stabilize the system or generate desirable chaos and it is shown that the system can be controlled by selecting appropriate control parameters. [ABSTRACT FROM AUTHOR]

In this paper, the Melnikov method for an abstract stochastic nonsmooth hybrid system is derived in detail and employed to study the homoclinic bifurcations and induced chaos in a bistable vibro-impact SD oscillator with bounded noise first proposed by Li et al. 2021, in which the geometric nonlinearity is used to produce the irrational restoring force and an impact map is introduced to describe energy loss during collisions. The initial Poincaré section is selected on the right rigid constraint so that rigorous perturbation analysis can be carried out to avoid the extension of trajectories near the switching manifold. The stochastic Melnikov function with geometrical intuition is obtained to detect the threshold of parameters for homocinic tangency of the perturbed stochastic stable and unstable manifolds by calculating the energy difference of their initial points on the Poincaré section. Finally, the analytical Melnikov analysis combined with numerical simulations is carried out to validate the developed Melnikov method for analyzing the global dynamics of the bistable vibro-impact SD oscillator subject to bounded noise. [ABSTRACT FROM AUTHOR]

Cellular automaton (CA) as a discrete and deterministic dynamic system has been widely used in cryptography. In this paper, a novel triple-coupling CA model is proposed. We first apply the triple-coupling model to 1D CA to design a high-quality pseudo-random number generator (PRNG). Numerical simulation and analyses show that triple-coupling CA exhibits more complex evolutionary behavior than uncoupling CA. The pseudo-random sequence generated by triple-coupling 1D CA can pass all NIST SP800-22 tests. Subsequently, the triple-coupling model is also applied to 2D CA, and a novel image encryption scheme based on this model is proposed. Thanks to the triple-coupling model, the diffusion operation can be completed between different color channels of the color image. Experimental simulations and extensive cryptanalysis show that the image encryption algorithm using the triple-coupling model has superior security and high efficiency. [ABSTRACT FROM AUTHOR]

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 and sequence need to be modified with amplitude and offset for a real application. In this paper, an initially-controlled double-scroll hyperchaotic map is constructed based on two sine functions. Four patterns of the double-scroll hyperchaotic orbits are found as 0-degree, 90-degree, 45-degree and 135-degree. Consequently, different modes for attractor growing are demonstrated. In this case, all the coexisting attractors are arranged in phase space in a direction defined by the initial value and the distance between two petals of any double-scroll orbit is adjusted. Finally, hardware experiments based on STM32 are carried out to verify the theoretical analysis and numerical simulation. [ABSTRACT FROM AUTHOR]

In this paper, we provide a new method for constructing chaotic Hopfield neural networks. Our approach is based on structuring the domain to form a special set through the discrete evolution of the network state variables. In the chaotic regime, the formed set is invariant under the system governing the dynamics of the neural network. The approach can be viewed as an extension of the unimodality technique for one-dimensional map, thereby generating chaos from higher-dimensional systems. We show that the discrete Hopfield neural network considered is chaotic in the sense of Devaney, Li–Yorke, and Poincaré. Mathematical analysis and numerical simulation are provided to confirm the presence of chaos in the network. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new four-dimensional hyperchaotic system derived from the chaotic maps of Peter de Jong's simple attractor and the discrete iterative function. In this work, our main motivation is to explore a link that can be developed to generate hyperchaos from 2D chaotic system. An association between 2D system and a higher order one was not studied in the previous literature. In fact, in the literature, there is no two-dimensional systems from which we are able to associate a four-dimensional one. In this context, a special interest is reserved to Peter de Jong system due to its exceptional advantages such as hypersensitivity and velocity. The challenge in this paper is the development of a four-dimensional hyperchaotic system associated to the Peter de Jong one while conserving its important characteristics such as hypersensitivity, velocity and the lack of equilibrium. The system structure that we will detail is different from other hyperchaotic systems widely suggested in the literature. In fact, the proposed attractor does not display any equilibrium point. A mathematical study is carried out in order to obtain time plots, Lyapunov exponents spectrum and bifurcation diagram. Finally, we will prove the high sensitivity of this system relative to its initial condition by simulations and experimental observations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the complex dynamical behaviors of a biological network that is derived from innate immune responses and that couples positive and negative feedback loops. The stability conditions of the non-negative equilibrium points (EPs) of the system are obtained, using the theory of dynamical systems, and we deduce that no more than three stable EPs exist in this system. Through bifurcation analysis and numerical simulations, we find that the system presents rich dynamical behaviors, such as monostability, bistability and oscillations. These results reveal how positive and negative feedback cooperatively regulate the dynamical behavior of the system. [ABSTRACT FROM AUTHOR]

In this paper, the synchronization problem of Chen systems with time-varying delays is discussed based on the stability theory of time-delay systems. Through the analysis of the error dynamical systems, the time-delay correlative synchronization controller is designed to achieve chaos synchronization. And finally, numerical simulations are provided to verify the effectiveness and feasibility of the developed method. [ABSTRACT FROM AUTHOR]

Variable-order fractional diffusion equation model is a recently developed and promising approach to characterize time-dependent or concentration-dependent anomalous diffusion, or diffusion process in inhomogeneous porous media. To further study the properties of variable-order time fractional subdiffusion equation models, the efficient numerical schemes are urgently needed. This paper investigates numerical schemes for variable-order time fractional diffusion equations in a finite domain. Three finite difference schemes including the explicit scheme, the implicit scheme and the Crank-Nicholson scheme are studied. Stability conditions for these three schemes are provided and proved via the Fourier method, rigorous convergence analysis is also performed. Two numerical examples are offered to verify the theoretical analysis of the above three schemes and illustrate the effectiveness of suggested schemes. The numerical results illustrate that, the implicit scheme and the Crank-Nicholson scheme can achieve high accuracy compared with the explicit scheme, and the Crank-Nicholson scheme claims highest accuracy in most situations. Moreover, some properties of variable-order time fractional diffusion equation model are also shown by numerical simulations. [ABSTRACT FROM AUTHOR]

The chaotic dynamics of fractional-order systems has attracted much attention recently. Chaotic synchronization of fractional-order systems is further studied in this paper. We investigate the chaos synchronization of two identical systems via a suitable linear controller applied to the response system. Based on the stability results of linear fractional-order systems, sufficient conditions for chaos synchronization of these systems are given. Control laws are derived analytically to achieve synchronization of the chaotic fractional-order Chen, Rössler and modified Chua systems. Numerical simulations are provided to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper we present a study of the influence of heterogeneity on the clustering of preferential attachment networks. The study is performed by the numerical analysis of the threshold preferential attachment model, a generalization of the Barabási—Albert model to heterogeneous complex networks. Heterogeneous networks are characterized by the existence of intrinsic properties of the nodes which induce specific affinities in their interactions. We analyze the influence of the affinity parameters on the distribution of degree-averaged clustering coefficients of the threshold model. We show that the introduction of heterogeneity increases the inverse correlation between clustering and connectivity of the nodes, inducing a power-law scaling in the clustering distribution. We also show that a higher level of heterogeneity increases the overall clustering coefficients irrespective of the node degrees. These results exhibit a better agreement of the extended model with the empirical observations of clustering in real networks. [ABSTRACT FROM AUTHOR]

This paper provides further results on bifurcation analysis of indirect field oriented control of induction motors. Previous results presented on this subject [Bazanella & Reginatto, 2000, 2001; Gordillo et al., 2002] are summarized and extended by means of a codimension-two bifurcation analysis. It is shown that codimension-two bifurcation phenomena, such as a Bogdanov–Takens and zero–Hopf bifurcations, occur in IFOC as a result of parameter mismatch and certain setting of the proportional-integral speed controller. Conditions for the existence of such bifurcations are derived analytically, as long as possible, and bifurcation diagrams are presented with the help of simulation and numerical bifurcation analysis. [ABSTRACT FROM AUTHOR]