Understanding the dynamics of interactions between antibiotic-resistant bacteria, the immune response, and the presence of antibiotics is crucial for developing effective strategies to combat antibiotic resistance. In this work, we introduce an innovative mathematical model that delves into the complex dynamics between bacteria that are resistant to antibiotics, the immune system, and the administration of antibiotic treatment. Through qualitative analysis, four distinct stable equilibria have been identified, each representing distinct biological scenarios, providing valuable insights for combating antibiotic resistance.

The current work proposes a hybrid data-driven model, consisting of convolutional neural networks (CNN) and convolutional long short-term memory (ConvLSTM), to enable an innovative application in prediction for microbeam's chaotic vibrations. In the proposed CNNConvLSTM model, CNN is used as feature extractor while ConvLSTM retains long-term connectivity across the entire sequence of frames. The flexibility and effectiveness of the model are demonstrated by its capability to perform both spatiotemporal and temporal processing. Specifically, the spatiotemporal model predicts the chaotic vibrations at 19 selected locations within the microbeam at a specific instant, while the temporal model predicts the microbeam's chaotic vibrations at a fixed location over time. Additionally, two conventional spatiotemporal models and three conventional temporal models are built for comparison, demonstrating the superior performance of CNNConvLSTM in terms of shorter training time and lower training and testing loss. The CNNConvLSTM model can provide useful guidance when investigating chaotic vibrations for performance enhancement and design optimization of microbeam-related devices.

Earthquake, petroleum and gas extraction, and underground nuclear test all could cause nonlinear tectonic deformation. It is of great significance to effectively predict and evaluate the disasters and impacts of these geological structure deformation. In this end, a three-dimension (3D) nonlinear elastodynamic sine–Gordon model that can be used to describe nonlinear tectonic deformation including 3D displacement vector, 3 × 3 symmetric stress tensor matrix, nonlinear sin term, and singular initial value functions is first proposed. Then, a new time semi-discrete mixed Crank–Nicolson (TSDMCN) scheme for the 3D nonlinear elastodynamic sine–Gordon model is developed, and the existence, stability, and error estimates of the TSDMCN solutions are proved. Next, a new two-grid mixed finite element Crank–Nicolson (TGMFECN) method with unconditional stability for the 3D nonlinear elastodynamic sine–Gordon model is developed, and the existence, stability, and error estimates of the TGMFECN solutions are proved. Thenceforth, it is the most important thing is that a novel reduced-dimensional iterative TGMFECN (RDITGMFECN) method in matrix form is established by resorting to proper orthogonal decomposition only to lower the unknown TGMFECN solution coefficient vectors and keep TGMFECN basis functions unchanged, which can ensure that the RDITGMFECN method has the same accuracy as the usual TGMFECN method, but can greatly lower the dimension of the unknown TGMFECN solution coefficient vectors so as to mitigate calculated workload, save CPU operating-time, improve computing efficiency, and improve real-time calculating accuracy. In theory, the existence, stability, and error estimates of RDITGMFECN solutions are demonstrated by matrix analysis such that the theoretical analysis becomes very intuitive and easy to be understood by the public, which is a new attempt of theoretical analysis. In application, two numerical examples are used to simulate the 3D nonlinear tectonic deformation caused by earthquake and to verify the correctness of our theoretical results and the effectiveness of the RDITGMFECN method.

In this manuscript, we present a globally divergence-free weak Galerkin finite element method with the IMEX-SAV scheme for solving the Kelvin–Voigt viscoelastic fluid flow model. Firstly, the weak Galerkin finite element method is used to analyze the spatial discretization, this method can yield globally divergence-free velocity solutions. Secondly, the IMEX-SAV difference scheme is adopted in the temporal discretization for the fully discrete scheme, and we can obtain the unconditional stability result for the velocity. In addition, combined with the stabilization idea, the method can not only reduce the spurious numerical oscillation at the high Reynolds number but also yield the uniform results that the constants in the error estimates do not explicitly depend on the inverse power of the physical parameters of the Kelvin–Voigt viscoelastic fluid flow model. Finally, several numerical experiments are performed to verify the theoretical results.

This paper investigates the finite-time synchronization (FTS) of complex dynamic networks (CDNs) with impulsive control subject to actuator saturation. We develop a novel method that integrates the impulsive comparison principle and improved convex hull representation lemma of saturated function to derive LMI-based sufficient conditions for FTS, which are easy to verify. We also estimate the admissible set of initial values to ensure the validity of the lemma. Unlike previous work, we relax the monotonicity assumption on the Lyapunov function, which broadens our results’ applicability. Moreover, we formulate and solve an optimization problem to enlarge the admissible set under the LMI constraints, using YALMIP toolbox in MATLAB software. Finally, several numerical examples are proposed to demonstrate our results’ effectiveness and superiority.

This article investigates adaptive event-triggered control for leader-following group consensus of hybrid heterogeneous multi-agent systems (HMASs) composed of single- and double-integrator agents under cooperative–competitive relationships. By using fully distributed control protocol and adaptive protocol, the leader-following group consensus can be achieved without global information. Additionally, a novel adaptive double dynamic event-triggered mechanism (DDETM) is proposed, in which two independent adaptive event-triggered conditions are devised to maintain events of communication and updates of controllers. Furthermore, adaptive parameters and internal dynamic variables are employed to reduce the number of triggers and exclude Zeno phenomenon. By utilizing Lyapunov stability theory, some sufficient conditions are acquired for the leader-following group consensus of the HMASs. Finally, simulation examples are given to prove the effectiveness of the proposed method.

This paper investigates the coupling dynamic characteristics of a double-beam structure with two linear oscillators that generate harmonic concentrated excitation and the vertical elastic support boundary, including the Sommerfeld effect and the synchronization behavior. The governing equations of motion with boundary conditions are developed using Hamilton's principle. The Sommerfeld effect near the resonance region is characterized by transient power balance analysis, and the critical power of the motor is given to allow the system to pass through the resonance region. The theoretical condition for the synchronous behavior of two linear oscillators is derived using the average method, and its stability is also determined. The synchronization characteristics are analyzed and compared with the numerical steady-state response of typical physical parameters. Results show good agreement. Further, on the condition of the linear oscillators exhibiting synchronous behavior, sensitive working regions and parameters are sought to suppress the dynamic loads transmitted from the system to the foundation. The parameter optimization results show that the stable phase difference plays a crucial role in vibration suppression within the appropriate range of sensitive parameters. This study effectively extends the theoretical criteria for synchronous behavior on complex structures and is expected to provide ideas for vibration suppression strategies of multi-driving sources acting on multi-groups of elastic structures.