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In this paper, a novel four-wing chaotic system is constructed based on the Sprott-A system. The novel system contains three nonlinearly quadratic terms, which have rich dynamics such as four-wing hidden attractors, hidden extreme multistability and transient transitions. It is found that this system has high complexity by spectral entropy analysis. In addition, a corresponding hardware analog circuit is designed based on this system by operational amplifiers and multipliers. The experimental results agree with those of the theoretical analysis and confirm that this system is practically feasible. This system will have a good application value in secure communication and cryptography. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behaviors of a discrete-time fractional-order population model are considered. The stability analysis and the topological classification of the model at the fixed point have been investigated. It is shown that the model undergoes flip and Neimark–Sacker bifurcations around the co-existence fixed point by using the bifurcation and the normal form theory. These bifurcations lead to chaos when the parameter changes at critical point. In order to control chaotic behavior in the model result from Neimark–Sacker bifurcation, the OGY feedback method has been used. Furthermore, some numerical simulations, including bifurcation diagrams, phase portraits and maximum Lyapunov exponents of the presented model are plotted to support the correctness of the analytical results. The positive Lyapunov exponents demonstrate that chaotic behavior exists in the considered model. [ABSTRACT FROM AUTHOR]

In view of the shortcomings of the existing reversible watermarking algorithms for encrypted images, such as low embedding rate and incomplete separation, and at the same time ensuring the embedding rate and the quality of the watermarked image, this paper proposes a reversible watermarking algorithm for encrypted images with high embedding rate and separable effect. This paper proposes a reversible watermarking algorithm for encrypted images with high embedding rate and separable effect. First, the plaintext image is encrypted by using the encryption series generated by chaotic system and Zu Chongzhi's encryption algorithm; Second, analyze the PSNR value of the image under different interpolation conditions, generate the corresponding expected interpolation, and embed the watermark information into the image based on the expected interpolation; Finally, the original image can be recovered by using the encryption key, and the watermark information can be obtained by using the embedded key. The security and embedding ability of the algorithm are analyzed through simulation experiments. The results show that the introduction of ZUC stream cipher can expand the key space of the algorithm, have high security and achieve the separable effect. The embedding of watermark information has little impact on the ciphertext image, and the embedding rate is also higher than the contrast algorithm under the condition of ensuring the visual effect of the image. [ABSTRACT FROM AUTHOR]

This paper explores a predator–prey system featuring fear and disease within the predator population,utilizing the Rosenzweig–MacArthur model with Holling type-II functional response. The primary focus lies in investigating the impact of a fear factor, wherein the prey's growth rate is hindered due to predator-induced fear. Additionally, the model accounts for the spread of disease among predators,leading to a division between susceptible and infected predator subpopulations. The inclusion of an Allee effect in the susceptible predator further enriches the model. The study involves a thorough examination, encompassing local and global stability analysis as well as Hopf bifurcation analysis around the interior equilibrium point. Numerical simulations underscore a noteworthy observation: an escalation in interaction force propels the system into chaotic dynamics,marked by stable focus, limit cycles and period-doubling phenomena. A noteworthy finding pertains to the influence of the Allee parameter (θ) on chaotic dynamics. As the Allee parameter values increase, the system tends to stable focus through a sequence of chaotic states, period-doubling and limit cycles. Subsequently, the paper introduces the role of another pivotal parameter, the fear factor, into the chaotic dynamics. Intriguingly, chaos transforms into stable focus through diverse nonlinear phenomena, including period-doubling and limit cycles. This nuanced exploration of parameters sheds light on the intricate dynamics governing the predator–prey system, offering a comprehensive understanding of the interplay between fear, disease and ecological factors. So our observation throughout this paper that how chaos behaves here after one by one injection of our new features: fear factor and Allee parameter? [ABSTRACT FROM AUTHOR]

The purpose of this paper is to analyze the dynamic characteristics and the meshing state transition characteristics of spalling defect gears under various lubrication conditions. The time-varying geometric parameters, motion parameters and load distribution of the gears in the state of positive meshing and reverse impact are analyzed. The time-varying meshing stiffness considering the time-varying friction coefficient under elastohydrodynamic lubrication (EHL), mixed lubrication and boundary lubrication are calculated, and the spalling defect is introduced in the stiffness calculation process. The equivalent lubrication model of the gear is established, the switching condition of the lubrication state is derived, and the distribution of the lubrication state in the torque-speed plane is discussed. The multimeshing state dynamic model of the spalling defect gear is established, and the evolution characteristics of the coexistence response and the transition of the meshing state under different lubrication conditions are simulated by using the attraction domain, phase trajectory, meshing force and bifurcation diagram. The results show that the phase trajectory of the gear with the spalling defect is deformed compared with that of the healthy gear. The change of lubrication state has little effect on the phase trajectory and attraction domain of the gear with spalling defect, but has a great influence on the meshing force. At the spalling boundary, the meshing force is changed abruptly, and the worse the lubrication state, the more obvious the mutation. Due to the influence of spalling on tooth stiffness, it will also affect the meshing force in the nonspalling area. [ABSTRACT FROM AUTHOR]

Memristor synapses have been widely introduced into neuronal models to investigate the effects of external magnetic fields. However, there is a relative lack of research on the external-induced electric fields in neurons. In this paper, a 4D-memristive Hindmarsh–Rose neuron model is constructed by introducing a memristor and an electric field variable, which can generate complex neural firing. Notably, numerical simulations reveal that the initial conditions of the memristor can induce different firing patterns, exhibiting a unique fractal structure in the basin of attractions. Remarkably, the offset parameters of the internal variables of the neuron can be canceled out so that the offset boosting of the variables can be achieved according to the initial values, giving rise to an uncountably many hidden attractors with homogeneous multistability. This model provides the first example of generating uncountably many attractors in a memristive neuron model without relying on trigonometric functions, significantly advancing our understanding of neuronal dynamics. Finally, a digital circuit is designed and implemented on the RISC-V platform to verify the numerical simulation and theoretical analysis. The findings of this study have a certain implication for the development of advanced neuromorphic computing systems and the understanding of complex neuronal behaviors in the presence of external electric fields. [ABSTRACT FROM AUTHOR]

This paper introduces a methodology for computing expected values associated with compression networks resulting from the application of compression algorithms to independent and identically distributed random time series. Our analysis establishes a robust correspondence between the calculated expected values and empirically derived results obtained from constructing networks using nondeterministic time series. Notably, the ratio of the average indegree of a network to the computed expected indegree for stochastic time series serves as a versatile metric. It enables the assessment of inherent randomness in time series and facilitates the distinction between nondeterministic and chaotic systems. The metric demonstrates high sensitivity to nondeterminism in both synthetic and real-world datasets, highlighting its capacity to detect subtle disturbances and high-frequency noise, even in series characterized by a deficient sample rate. Our results extend and confirm previous findings in the field. [ABSTRACT FROM AUTHOR]

In this paper, we explore the rich dynamics in the Chen system using Runge–Kutta method and Deep Neural Networks (DNNs). Compared with the Lorenz system, we find that the first return map P of the Chen system exhibits a more complex structure of continuous regions in the Poincaré section. Moreover, the existence of six crossing blocks with respect to the second return map implies that there is a closed invariant set Λ in the Poincaré section such that P 2 | Λ is semi-conjugate to a 6-shift map, thus demonstrating remarkably chaos in the Chen system. [ABSTRACT FROM AUTHOR]

In this paper, we detect Unstable Periodic Orbits (UPOs) of both self-excited and hidden attractors using the Damped Newton–Raphson–Mees algorithm. This study answers one of the long-standing questions about the size of a hidden attractor. We observe that the UPOs of the self-excited attractor are spread in a thick region within the phase space at varying distances from the fixed point, whereas the UPOs of hidden attractors are confined to a thin layer. This reveals details concerning the size of a hidden attractor. We demonstrate this for a hidden attractor without a fixed point and for a hidden attractor with a single stable fixed point. To compare the results with self-excited attractors, we have taken Lorenz and Rössler attractor as examples. [ABSTRACT FROM AUTHOR]

In this paper, we propose a host–parasitoid model with a Holling type-II functional response and incorporate harvest effort. The Holling type-II response leads to saturation in parasitized hosts, creating a potential economic harvesting opportunity. To address overexploitation risks, we integrate a harvest effort function, determining an optimal threshold to prevent depletion. We explore model dynamics and bifurcations, including co-dimension one behaviors such as flip and Neimark–Sacker bifurcations, we provide numerical examples for validation. Our suggested difference-algebraic model, compared to continuous-time models, exhibits rich dynamics within the Nicholson–Bailey host–parasitoid framework. [ABSTRACT FROM AUTHOR]

This paper presents a novel discrete memristor model that incorporates exponential and absolute value functions. A discrete coupled memristor neural network model is constructed based on this memristor design. The periodic and chaotic regions of the discrete neural network model are determined using bifurcation and Lyapunov exponent spectrum. Furthermore, by varying the initial values of the discrete memristive neural network, we observe the coexistence of chaos and periodic attractors, as well as periodic attractors. Additionally, an application to color image encryption based on the discrete system model is given. Security analysis is conducted in the aspects of key space, histogram analysis, correlation analysis, sensitivity analysis, Peak Signal-to-Noise Ratio (PSNR), and information entropy analysis. The analysis results show that the algorithm has a key space size of 2 2 5 8 , and the information entropy of baboon graph is 7.9993, which is very close to the ideal value of 8. It shows that the image encryption algorithm is feasible and effective. Finally, the implementation of the discrete memristive neural network model is realized using Field Programmable Gate Array (FPGA). The experimental implementation is conducted using the Verilog language on the Vivado 2018.3 platform, and the obtained results align with the numerical simulation results obtained through MATLAB. [ABSTRACT FROM AUTHOR]

This paper investigates the nonlinear bifurcation and chaos characteristics of piezoelectric composite lattice sandwich plates at 1:3 internal resonance. The nonlinear vibration partial differential equation is first discretized to become an ordinary differential equation by applying the Galerkin method. The main resonance modulation equations and the parametric resonance for the external excitation frequency that is close to the system's second-order modal frequency are then obtained by using the multiscale method. The Newton–Raphson method is subsequently applied to obtain the bifurcation diagram of the steady-state equilibrium of modulation equation with varying system parameters. The equilibrium stability is finally analyzed. We confirm the existence of static bifurcation such as saddle-node bifurcation, pitchfork bifurcation, and Hopf dynamic bifurcation. A detailed analysis is also conducted on the complex nonlinear jump phenomenon caused by the presence of multiple nonlinear steady-state solution regions. In the dynamic Hopf bifurcation interval, the fourth-order Runge–Kutta method is used to continue to track the dynamic periodic solution of the modulation equation in Cartesian coordinates. It is found that there are multiple boundary crises and attractor merging crises in the vibration system for piezoelectric composite lattice sandwich plates. [ABSTRACT FROM AUTHOR]

Deep Neural Networks (DNNs) have been successfully applied to investigations of numerical dynamics of finite-dimensional nonlinear systems such as ODEs instead of finding numerical solutions to ODEs via the traditional Runge–Kutta method and its variants. To show the advantages of DNNs, in this paper, we demonstrate that the DNNs are more efficient in finding topological horseshoes in chaotic dynamical systems. [ABSTRACT FROM AUTHOR]

In real-world networks, due to complex topological structures and uncertainties such as time delays, uncontrolled systems may generate instability and complexity, thereby degrading network performance. This paper provides a detailed analysis of the stability, Hopf bifurcation, and complex dynamics of a networked system under delayed feedback control. Based on the linear stability method and Hopf bifurcation theorem, the stability of the equilibrium of the error system and the existence of Hopf bifurcation are studied. The stability of periodic solutions bifurcating from the trivial equilibrium is analyzed using normal form theory and central manifold theorem. Special focus is on the effects of the network topology and time delays on the stability and Hopf bifurcation. The theoretical results are also extended to the complex networks with asymmetric adjacent matrices. In addition, the controlled model exhibits complicated dynamical behavior via three types of codimension two bifurcations and period-doubling bifurcations that eventually lead to chaos. Numerical experiments have validated the theoretical results and indicated that delayed feedback control can effectively generate or annihilate the complicated behavior of complex networks. [ABSTRACT FROM AUTHOR]