Dynamic properties of the coupled Oregonator model with delay

This work explores a coupled Oregonator model. By analyzing the associated characteristic equation, linear stability is investigated and Hopf bifurcations are demonstrated, as well as the stability and direction of the Hopf bifurcation are determined by employing the normal form method and the center manifold reduction. We also discussed the Z2 equivariant property and the existence of multiple periodic solutions. Numerical simulations are presented to illustrate the results in Section 5

Dynamic analysis of a Leslie–Gower-type predator–prey system with the fear effect and ratio-dependent Holling III functional response

In this paper, we extend a Leslie–Gower-type predator–prey system with ratio-dependent Holling III functional response considering the cost of antipredator defence due to fear. We study the impact of the fear effect on the model, and we find that many interesting dynamical properties of the model can occur when the fear effect is present. Firstly, the relationship between the fear coefficient K and the positive equilibrium point is introduced. Meanwhile, the existence of the Turing instability, the Hopf bifurcation, and the Turing–Hopf bifurcation are analyzed by some key bifurcation parameters. Next, a normal form for the Turing–Hopf bifurcation is calculated. Finally, numerical simulations are carried out to corroborate our theoretical results

Hopf-pitchfork bifurcation of coupled van der Pol oscillator with delay

In this paper, the Hopf-pitchfork bifurcation of coupled van der Pol with delay is studied. The interaction coefficient and time delay are taken as two bifurcation parameters. Firstly, the normal form is gotten by performing a center manifold reduction and using the normal form theory developed by Faria and Magalhães. Secondly, bifurcation diagrams and phase portraits are given through analyzing the unfolding structure. Finally, numerical simulations are used to support theoretical analysis

Hopf-zero bifurcation of the ring unidirectionally coupled Toda oscillators with delay

In this paper, the Hopf-zero bifurcation of the ring unidirectionally coupled Toda oscillators with delay was explored. First, the conditions of the occurrence of Hopf-zero bifurcation were obtained by analyzing the distribution of eigenvalues in correspondence to linearization. Second, the stability of Hopf-zero bifurcation periodic solutions was determined based on the discussion of the normal form of the system, and some numerical simulations were employed to illustrate the results of this study. Lastly, the normal form of the system on the center manifold was derived by using the center manifold theorem and normal form method

Steady-state bifurcation of FHN-type oscillator on a square domain

The Turing patterns of reaction-diffusion equations defined over a square region are more complex because of the D4-symmetry of the spatial region. This leads to the occurrence of multiple equivariant Turing bifurcations. In this paper, taking the FHN model as an example, we give a explicit calculation formula of normal form for the simple and double Turing bifurcation of the reaction-diffusion equation with Dirichlet boundary conditions and defined on a square space, and we also obtain a method for the calculation of the existence of spatially inhomogeneous steady-state solutions. This paper provides a theoretical basis for exploring and predicting the pattern formation of spatial multimode interaction

SVD-based Method for Radio Frequency Interference Suppression Applied to SAR

Synthetic aperture radar (SAR) is a special type of active microwave sensor, which has got a wide range of applications in remote sensing. However, the performance of SAR systems may be affected by radio frequency interference (RFI) in several geographic regions. A novel singular value decomposition method is proposed for radio frequency interference suppression applied to SAR. This method decomposes the singular vectors of the received signal with RFI into interference subspace and signal subspace. The orthogonality of the two subspaces is used to suppress the RFI. The point-target simulation is used to show the working principle of the proposed algorithm. The experimental results based on SAR real data are also shown to verify the proposed algorithm.Defence Science Journal, 2012, 62(2), pp.132-136, DOI:http://dx.doi.org/10.14429/dsj.62.114

De novo acute megakaryoblastic leukemia with p210 BCR/ABL and t(1;16) translocation but not t(9;22) Ph chromosome

Acute megakaryoblastic leukemia (AMKL) is a type of acute myeloid leukemia (AML), in which majority of the blasts are megakaryoblastic. De novo AMKL in adulthood is rare, and carries very poor prognosis. We here report a 45-year-old woman with de novo AMKL with BCR/ABL rearrangement and der(16)t(1;16)(q21;q23) translocation but negative for t(9;22) Ph chromosome. Upon induction chemotherapy consisting of homoharringtonine, cytarabine and daunorubicin, the patient achieved partial hematological remission. The patient was then switched to imatinib plus one cycle of CAG regimen (low-dose cytarabine and aclarubicin in combination with granulocyte colony-stimulating factor), and achieved complete remission (CR). The disease recurred after 40 days and the patient eventually died of infection. To the best of our knowledge, this is the first report of de novo AMKL with p210 BCR/ABL and der(16)t(1;16)(q21;q23) translocation but not t(9;22) Ph chromosome

SCSC: Spatial Cross-scale Convolution Module to Strengthen both CNNs and Transformers

This paper presents a module, Spatial Cross-scale Convolution (SCSC), which is verified to be effective in improving both CNNs and Transformers. Nowadays, CNNs and Transformers have been successful in a variety of tasks. Especially for Transformers, increasing works achieve state-of-the-art performance in the computer vision community. Therefore, researchers start to explore the mechanism of those architectures. Large receptive fields, sparse connections, weight sharing, and dynamic weight have been considered keys to designing effective base models. However, there are still some issues to be addressed: large dense kernels and self-attention are inefficient, and large receptive fields make it hard to capture local features. Inspired by the above analyses and to solve the mentioned problems, in this paper, we design a general module taking in these design keys to enhance both CNNs and Transformers. SCSC introduces an efficient spatial cross-scale encoder and spatial embed module to capture assorted features in one layer. On the face recognition task, FaceResNet with SCSC can improve 2.7% with 68% fewer FLOPs and 79% fewer parameters. On the ImageNet classification task, Swin Transformer with SCSC can achieve even better performance with 22% fewer FLOPs, and ResNet with CSCS can improve 5.3% with similar complexity. Furthermore, a traditional network (e.g., ResNet) embedded with SCSC can match Swin Transformer's performance.Comment: ICCV2023 Workshop (New Ideas in Vision Transformers

Dynamic Properties of Coupled Maps

Dynamic properties are investigated in the coupled system of three maps with symmetric nearest neighbor coupling and periodic boundary conditions. The dynamics of the system is controlled by certain coupling parameters. We show that, for some values of the parameters, the system exhibits nontrivial collective behavior, such as multiple bifurcations, and chaos. We give computer simulations to support the theoretical predictions

Forest model dynamics analysis and optimal control based on disease and fire interactions

Three models for the propagation of forest disease are revisited to include the effect of forest fires and disease spread. We study the global stability of the forest-disease model in the absence of forest fires and the spread of disease. When forest fires caused by grass cover are considered, we show that the equilibrium points are locally asymptotically stable. If both forest fires and the spread of disease exist in the second model, then Turing instability can occur. In this case, the system exhibits complex dynamic behavior. To determine the effect of fire on the forest disease model, we obtain the optimal control expression of the key parameter fire factor, and carry out sensitivity analysis. Finally, we use forest biomass data of some provinces in China from 2002 to 2018 for numerical simulation, and the results are in agreement with the theoretical analysis