This paper proposes a novel singularity-free prescribed-time distributed resource allocation algorithm. By scaling fixed-time systems using the time space deformation method, the proposed algorithm avoids the singularity problem caused by time-varying high-gain functions. To make the algorithm applicable to second-order multi-agent systems, a singularity-free prescribed-time signal tracking controller is also proposed. Finally, the performance of the proposed algorithm is verified through a power allocation task based on actual wind farm data.

In this study, we explore the projective synchronization of quaternion-valued competitive neural networks with multiple time scales (QVMTSCNNs), while analyzing the impacts of discontinuous activation functions and time delays. To achieve the control goal, two novel quaternion controllers are designed, which do not depend on the ratio of the fast and slow time scales. By applying the nonsmooth analysis and quaternion inequality techniques, two novel theorems for projective synchronization of QVMTSCNNs are derived by non-separating methods. The obtained results in this study are relatively simpler and straightforward, extending some previous findings. Lastly, numerical analyses are executed to substantiate the theoretical conclusions.

This paper focuses on fixed-time synchronization (FTS) and preassigned-time synchronization (PTS) of bidirectional associative memory memristive neural networks (BAMMNNs) with mixed-time delays via event-triggered control (ETC). Firstly, by using Lyapunov stability theory, fixed/preassigned-time stability lemmas and inequality techniques, results on FTS and PTS of BAMMNNs are derived. Secondly, compared to asymptotic synchronization and finite-time synchronization, the FTS and PTS studied here achieve faster convergence speeds and more precise settling times. Thirdly, the model incorporates state switching, time-varying and distributed delays; specifically, the time delays do not require differentiability, which enhances the generality of the results. Additionally, a segmented ETC strategy is designed to suit the dual-layer structure of BAMMNNs, where control actions are executed based on set triggering conditions, thus significantly reducing information transmission power consumption. Finally, a numerical simulation example is provided to verify the correctness of the results.

Dynamical systems are complex and constantly changing systems that exhibit predictable and unpredictable behaviour because of their inherent randomness and sensitivity to initial conditions. In the last few years, the dynamics of various fixed-point recursive methods and chaotic maps have received significant attention from the research community. Generally, in dynamical systems, the standard dynamics revolve around the chaotic map λp(1 − p), where the growth rate parameter λ ∈ [0, 4]. In this article, a novel Geometric Mean-Based fixed point recursive method is used to examine the dynamical behaviour in the chaotic map λp(1 − p) in which the growth rate parameter λ ∈ [0, 4] approaches a maximum value of 6.7. Furthermore, the mathematical and computational study reveals the efficiency of the proposed approximation method. In this method, the logistic map admits extra freedom in the parameter λ, which gives improved dynamic properties such as fixed point, periodicity, chaos, and Lyapunov exponent. Additionally, it has been noted that better dynamic performance could enhance various applications such as weather forecasting, secure communications, neural networks, cryptography, and discrete traffic flow models, etc.