A neuro swarm procedure to solve the novel second order perturbed delay Lane-Emden model arising in astrophysics

Abstract

The current work provides a mathematical second order perturbed singular delay differential model (SO-PSDDM) by using the standard form of the Lane-Emden model. The inclusive structures based on the delay terms, singular-point and perturbation factor and shape forms of the SO-PSDDM are provided. The novel form of the SO-PSDDM is numerically solved by using the procedures of artificial neural networks (ANNs) along with the optimization measures based on the swarming procedures (PSO) and interior-point algorithm (IPA). An error function is optimized through the swarming PSO procedure along with the IPA to solve the SO-PSDDM. The precision, substantiation and validation are observed for three problems of the SO-PSDDM. The exactness of the novel SO-PSDDM is observed by comparing the obtained and exact solutions. The reliability, stability and convergence of the proposed stochastic algorithms are observed for 30 independent trials to solve the novel SO-PSDDM.

A general description of criticality in neural network models

“…Previous animal studies both in vitro and in vivo, together with computational modeling, have strongly suggested that the avalanche dynamics in neural systems may arise at the critical state in excitation–inhibition balanced networks and can be regulated by several intrinsic network properties, such as short-term synaptic plasticity and the balance level between excitation and inhibition [2] , [17] , [20] . With the help of simulating the stochastic dynamical model, we can fully understand the underlying mechanism of biological phenomena [29] , [28] . Jingwen's results demonstrate that the coordinated dynamics of criticality and asynchronous dynamics can be generated by the same neural system if excitatory and inhibitory synapses are tuned appropriately [18] .…”

Dragonfly visual evolutionary neural network: A novel bionic optimizer with related LSGO and engineering design optimization

“…With the rapid development of big data and artificial intelligence, various engineering design optimization problems with unknown large-scale parameters increase exponentially, e.g., Li-ion battery health prediction, 1 offline time-sensitive load scheduling, 2 railway passenger network operation, 3 optimal clustering design, 4 remote sensing images, 5 electronic system design, 6 deep neural networks, 7 diagnosis of COVID-19, 8 community acquired pneumonia, 9 the second-order perturbation delay Lane–Emden model in astrophysics, 10 the fifth type of induction motor model, 11 etc. Even though such problems can be well expressed by LSGO models, they will face a great challenge when solving their optima due to complex variables interaction or hard constraints.…”