Comparative exploration on bifurcation behavior for integer-order and fractional-order delayed BAM neural networks

In the present study, we deal with the stability and the onset of Hopf bifurcation of two type delayed BAM neural networks (integer-order case and fractional-order case). By virtue of the characteristic equation of the integer-order delayed BAM neural networks and regarding time delay as critical parameter, a novel delay-independent condition ensuring the stability and the onset of Hopf bifurcation for the involved integer-order delayed BAM neural networks is built. Taking advantage of Laplace transform, stability theory and Hopf bifurcation knowledge of fractional-order differential equations, a novel delay-independent criterion to maintain the stability and the appearance of Hopf bifurcation for the addressed fractional-order BAM neural networks is established. The investigation indicates the important role of time delay in controlling the stability and Hopf bifurcation of the both type delayed BAM neural networks. By adjusting the value of time delay, we can effectively amplify the stability region and postpone the time of onset of Hopf bifurcation for the fractional-order BAM neural networks. Matlab simulation results are clearly presented to sustain the correctness of analytical results. The derived fruits of this study provide an important theoretical basis in regulating networks

Binary Star Evolution in Different Environments: Filamentary, Fractal, Halo and Tidal-tail Clusters

Using membership of 85 open clusters from previous studies (Pang et al. 2021a,b, 2022b; Li et al. 2021) based on Gaia DR3 data, we identify binary candidates in the color-magnitude diagram, for systems with mass ratio q > 0.4. The binary fraction is corrected for incompleteness at different distances due to the Gaia angular resolution limit. We find a decreasing binary fraction with increasing cluster age, with substantial scatter. For clusters with a total mass > 200$M_\odot$, the binary fraction is independent of cluster mass. The binary fraction depends strongly on stellar density. Among four types of cluster environments, the lowest-density filamentary and fractal stellar groups have the highest mean binary fraction: 23.6% and 23.2%, respectively. The mean binary fraction in tidal-tail clusters is 20.8%, and is lowest in the densest halo-type clusters: 14.8%. We find clear evidence of early disruptions of binary stars in the cluster sample. The radial binary fraction depends strongly on the cluster-centric distance across all four types of environments, with the smallest binary fraction within the half-mass radius $r_h$, and increasing towards a few $r_h$. Only hints of mass segregation is found in the target clusters. The observed amount of mass segregation is not significant to generate a global effect inside the target clusters. We evaluate the bias of unresolved binary systems (assuming a primary mass of 1$M_\odot$) in 1D tangential velocity, which is 0.1-1$\,\rm km\,s^{-1}$. Further studies are required to characterize the internal star cluster kinematics using Gaia proper motions

Riemann problem for a compressible perfect fluid with a constant external force for the Chaplygin gas

Abstract The Riemann problem for a compressible perfect fluid with a constant external force for the Chaplygin gas is considered. We obtain two kinds of exact solutions. The first one consists of contact discontinuities, while the other one involves a delta shock wave in which both density and internal energy contain a Dirac delta function. The position, speed and weights of the delta shock wave are derived from both generalized Rankine–Hugoniot relation and entropy condition, which are established in detail. Moreover, the solutions are no longer self-similar due to the influence of the constant external force

Bifurcation Behavior and Hybrid Controller Design of a 2D Lotka–Volterra Commensal Symbiosis System Accompanying Delay

All the time, differential dynamical models with delay has witness a tremendous application value in characterizing the internal law among diverse biological populations in biology. In the current article, on the basis of the previous publications, we formulate a new Lotka–Volterra commensal symbiosis system accompanying delay. Utilizing fixed point theorem, inequality tactics and an appropriate function, we gain the sufficient criteria on existence and uniqueness, non-negativeness and boundedness of the solution to the formulated delayed Lotka–Volterra commensal symbiosis system. Making use of stability and bifurcation theory of delayed differential equation, we focus on the emergence of bifurcation behavior and stability nature of the formulated delayed Lotka–Volterra commensal symbiosis system. A new delay-independent stability and bifurcation conditions on the model are presented. By constructing a positive definite function, we explore the global stability. By constructing two diverse hybrid delayed feedback controllers, we can adjusted the domain of stability and time of appearance of Hopf bifurcation of the delayed Lotka–Volterra commensal symbiosis system. The effect of time delay on the domain of stability and time of appearance of Hopf bifurcation of the model is given. Matlab experiment diagrams are provided to sustain the acquired key outcomes

AI-based MRI auto-segmentation of brain tumor in rodents, a multicenter study

Abstract Automatic segmentation of rodent brain tumor on magnetic resonance imaging (MRI) may facilitate biomedical research. The current study aims to prove the feasibility for automatic segmentation by artificial intelligence (AI), and practicability of AI-assisted segmentation. MRI images, including T2WI, T1WI and CE-T1WI, of brain tumor from 57 WAG/Rij rats in KU Leuven and 46 mice from the cancer imaging archive (TCIA) were collected. A 3D U-Net architecture was adopted for segmentation of tumor bearing brain and brain tumor. After training, these models were tested with both datasets after Gaussian noise addition. Reduction of inter-observer disparity by AI-assisted segmentation was also evaluated. The AI model segmented tumor-bearing brain well for both Leuven and TCIA datasets, with Dice similarity coefficients (DSCs) of 0.87 and 0.85 respectively. After noise addition, the performance remained unchanged when the signal–noise ratio (SNR) was higher than two or eight, respectively. For the segmentation of tumor lesions, AI-based model yielded DSCs of 0.70 and 0.61 for Leuven and TCIA datasets respectively. Similarly, the performance is uncompromised when the SNR was over two and eight respectively. AI-assisted segmentation could significantly reduce the inter-observer disparities and segmentation time in both rats and mice. Both AI models for segmenting brain or tumor lesions could improve inter-observer agreement and therefore contributed to the standardization of the following biomedical studies