Quantifying the potential of cascade outbreaks via early infected nodes using network percolation.

In many fields, accurate prediction of cascade outbreaks during their early stages of propagation is of paramount importance. Based on percolation theory, we propose a global propagation probability algorithm that effectively estimates the probability of information spreading from source nodes to the giant component. Building on this, we further introduce an early prediction method for cascade outbreaks, which provides quantitative predictions of both the probability and scope of cascade outbreaks by fully considering the network structure data and propagation dynamics. Through our research, we observe that cascade outbreaks resemble a phase transition. When approaching the critical point of an outbreak, a few specific activating nodes typically facilitate the transmission of information throughout the entire network, thus enabling early inference of a cascading outbreak. To validate our findings, we conducted experiments on diverse network structures using a classical propagation model and applied our proposed method to analyze a real microblog cascade dataset. The experimental results robustly demonstrate the superiority of our approach over baseline methods in terms of effectively predicting cascade outbreaks with high precision and early detection capability.

[Cystic fibrosis primarily presenting with pseudo-Bartter syndrome: a report of three cases and literature review]. / 以假性Bartter综合征为主要表现的囊性纤维化患儿3ä¾‹å¹¶æ–‡çŒ®å¤ä¹ .

OBJECTIVES: To summarize the clinical characteristics and genetic variations in children with cystic fibrosis (CF) primarily presenting with pseudo-Bartter syndrome (CF-PBS), with the aim to enhance understanding of this disorder. METHODS: A retrospective analysis was performed on the clinical data of three children who were diagnosed with CF-PBS in Hunan Children's Hospital from January 2018 to August 2023, and a literature review was performed. RESULTS: All three children had the onset of the disease in infancy. Tests after admission showed hyponatremia, hypokalemia, hypochloremia, and metabolic alkalosis, and genetic testing showed the presence of compound heterozygous mutation in the CFTR gene. All three children were diagnosed with CF. Literature review obtained 33 Chinese children with CF-PBS, with an age of onset of 1-36 months and an age of diagnosis of 3-144 months. Among these children, there were 29 children with recurrent respiratory infection or persistent pneumonia (88%), 26 with malnutrition (79%), 23 with developmental retardation (70%), and 18 with pancreatitis or extrapancreatic insufficiency (55%). Genetic testing showed that c.2909G>A was the most common mutation site of the CFTR gene, with a frequency of allelic variation of 23% (15/66). CONCLUSIONS: CF may have no typical respiratory symptoms in the early stage. The possibility of CF-PBS should be considered for infants with recurrent hyponatremia, hypokalemia, hypochloremia, and metabolic alkalosis, especially those with malnutrition and developmental retardation. CFTR genetic testing should be performed as soon as possible to help with the diagnosis of CF.

Novel Loss of Function (G15D) Mutation on RAC2 in a Family with Combined Immunodeficiency and Increased Levels of Immunoglobulin G, A, and E.

Ras-related C3 botulinum toxin substrate 2 (RAC2) is a small guanine nucleotide binding molecule that is exclusively expressed in hematopoietic cell lineages as a switcher. Based on in vivo and/or in vitro model experiments, RAC2 plays important roles in different cells through proliferation, secretion, and phagocytosis. It also performs a suppressing function in immunoglobulin (Ig) switching in Rac2-/- animals or cells. Several RAC2 natural mutations have been described in patients with primary immunodeficiency. RAC2 mutations can be classified into loss-of-function inactivating (LoF-I) and gain-of-function activating mutations according to their functional effects. Only two LoF-I mutations on RAC2 have been reported, including a dominant D57N mutation in several cases that exhibit granulocyte function defects and a recessive D56X mutation in cases with common variable immunodeficiency. Regardless of the type of mutation, most of the reported RAC2 mutant cases have shown reduced IgG, IgA, and IgM levels. Herein, we report on a family with three members that suffer from persistent HPV infection, recurrent respiratory infections, bronchiectasis, and autoimmune disease. The immunologic profile suggests that the family was affected by combined immunodeficiency (CID) with increased serum levels of IgG, IgA, and IgE. Exome sequencing identified a de novo RAC2 mutation (c.44G > A/p.G15D) that was co-segregated with the disease in the family. Gene functional experiments identified that such mutation results in reduced guanosine triphosphate binding activity and RAC2 protein expression. In patients' lymphocytes, impaired aggregation and proliferation effects, decreased mitochondrial membrane potential, and increased levels of cell apoptosis were observed, although no functional abnormalities were detected in neutrophils. To our knowledge, this study was the first to identify a LoF-I mutation of RAC2 affecting lymphocyte function that consequently led to CID and increased levels of serum IgG, IgE, and IgA. This study presents a novel subtype of RAC2-related immune disorder.

Impact of Allee and fear effects in a fractional order prey-predator system with group defense and prey refuge.

This paper presents a novel fractional-order model of a prey-predator system that incorporates group defense and prey refuge mechanisms, along with Allee and fear effects. First, we examine the existence, uniqueness, non-negativity, and boundedness of the solution of the system. Second, a comprehensive analysis is conducted on the existence, stability, and coexistence of equilibrium states in the system, which are crucial for comprehending prey-predator system behavior. Our investigation reveals that the coexistence equilibrium undergoes a Hopf bifurcation under five key parameters. Specifically, an increased threshold for the transition between group and individual behavior, influenced by different strengths of the Allee effect, enhances the stability of both populations. This discovery sheds light on the role of group effects in shaping prey-predator interactions and ecosystem stability. Third, system discretization is employed to explore the impact of step size on stimulating stability and to investigate the Neimark-Sacker bifurcation, providing a more comprehensive understanding of system behavior. The role of step size as a constraint on stability is examined, revealing the system's progression from stability to chaos. Consequently, our results offer a more flexible mechanism for adjusting the stability and dynamics of the two species. Finally, numerical simulations are utilized to validate the reasonableness of the research findings.

Robustness measurement of multiplex networks based on graph spectrum.

Networks can provide effective representations of the relationships between elements in complex systems through nodes and links. On this basis, relationships between multiple systems are often characterized as multilayer networks (or networks of networks). As a typical representative, a multiplex network is often used to describe a system in which there are many replaceable or dependent relationships among elements in different layers. This paper studies robustness measures for different types of multiplex networks by generalizing the natural connectivity calculated from the graph spectrum. Experiments on model and real multiplex networks show a close correlation between the robustness of multiplex networks consisting of connective or dependent layers and the natural connectivity of aggregated networks or intersections between layers. These indicators can effectively measure or estimate the robustness of multiplex networks according to the topology of each layer. Our findings shed new light on the design and protection of coupled complex systems.

Arthroscopic treatment of ankle impingement syndrome.

Arthroscopic treatment of ankle impingement syndrome (AIS) is a minimally invasive surgical procedure used to address symptoms caused by impingement in the ankle joint. This syndrome occurs when there is abnormal contact between certain bones or soft tissues in the ankle, leading to pain, swelling, or limited range of motion. Traditionally, open surgery was the standard approach for treating AIS. However, with advancements in technology and surgical techniques, arthroscopic treatment has become a preferred method for many patients and surgeons. With improved visualization and precise treatment of the arthroscopy, patients can experience reduced pain and improved functionality, allowing them to return to their daily activities sooner. In this paper, we reviewed the application and clinical efficacy the of arthroscopic approach for treating AIS, hoping to provide a reference for its future promotion.

Twist2 Reduced NLRP3-Induced Inflammation of Infantile Pneumonia via Regulation of Mitochondrial Permeability Transition by FOXO1.

BACKGROUND: Infantile pneumonia is an acute inflammatory lesion of the lung caused by mycoplasma pneumonia. Indeed, Twist2 signaling pathway controls inflammatory reaction, oxidative stress, and other biological reaction. However, the regulation of Twist2 on the inflammation in infantile pneumonia remains unclear. This study explained that the function and mechanism of Twist2 in infantile pneumonia. METHODS: The subjects included the serum samples of 12 patients with infantile pneumonia and normal healthy volunteers from Hunan Children's Hospital. Besides, mice were given with lipopolysaccharide (LPS) into the lung. Moreover, RAW264.7 macrophages were stimulated with LPS for 4 h and added to the culture medium. RESULTS: In present study, in serum of patients with infantile pneumonia or lung tissue of mice model with infantile pneumonia, TWIST2 expression was lessened. Apart from that, TWIST2 protein could reduce the inflammatory reaction in mice model with infantile pneumonia, resulting in an inhibition in lung injury. Conversely, over-expression of TWIST2 also decreased inflammatory reaction in macrophages model via the regulation of FOXO1/NLRP3 pathway. Downregulation of TWIST2 promoted the inflammation in macrophages model by the regulation of FOXO1/NLRP3 pathway. CONCLUSION: According to the findings, present study have identified that the TWIST2 could reduce the inflammation of infantile pneumonia by NLRP3 inflammasome through the regulation of mitochondrial permeability transition and the induction of FOXO1 expression.

The structure inference of flocking systems based on the trajectories.

The interaction between the swarm individuals affects the dynamic behavior of the swarm, but it is difficult to obtain directly from outside observation. Therefore, the problem we focus on is inferring the structure of the interactions in the swarm from the individual behavior trajectories. Similar inference problems that existed in network science are named network reconstruction or network inference. It is a fundamental problem pervading research on complex systems. In this paper, a new method, called Motion Trajectory Similarity, is developed for inferring direct interactions from the motion state of individuals in the swarm. It constructs correlations by combining the similarity of the motion trajectories of each cross section of the time series, in which individuals with highly similar motion states are more likely to interact with each other. Experiments on the flocking systems demonstrate that our method can produce a reliable interaction inference and outperform traditional network inference methods. It can withstand a high level of noise and time delay introduced into flocking models, as well as parameter variation in the flocking system, to achieve robust reconstruction. The proposed method provides a new perspective for inferring the interaction structure of a swarm, which helps us to explore the mechanisms of collective movement in swarms and paves the way for developing the flocking models that can be quantified and predicted.

Change point detection in multi-agent systems based on higher-order features.

Change point detection (CPD) for multi-agent systems helps one to evaluate the state and better control the system. Multivariate CPD methods solve the d × T time series well; however, the multi-agent systems often produce the N × d × T dimensional data, where d is the dimension of multivariate observations, T is the total observation time, and N is the number of agents. In this paper, we propose two valid approaches based on higher-order features, namely, the Betti number feature extraction and the Persistence feature extraction, to compress the d-dimensional features into one dimension so that general CPD methods can be applied to higher-dimensional data. First, a topological structure based on the Vietoris-Rips complex is constructed on each time-slice snapshot. Then, the Betti number and persistence of the topological structures are obtained to separately constitute two feature matrices for change point estimates. Higher-order features primarily describe the data distribution on each snapshot and are, therefore, independent of the node correspondence cross snapshots, which gives our methods unique advantages in processing missing data. Experiments in multi-agent systems demonstrate the significant performance of our methods. We believe that our methods not only provide a new tool for dimensionality reduction and missing data in multi-agent systems but also have the potential to be applied to a wider range of fields, such as complex networks.

Comprehensive Analysis of FASN in Tumor Immune Infiltration and Prognostic Value for Immunotherapy and Promoter DNA Methylation.

Fatty acid synthase (FASN) promotes tumor progression in multiple cancers. In this study, we comprehensively examined the expression, prognostic significance, and promoter methylation of FASN, and its correlation with immune cell infiltration in pan-cancer. Our results demonstrated that elevated FASN expression was significantly associated with an unfavorable prognosis in many cancer types. Furthermore, FASN promoter DNA methylation can be used as a tumor prognosis marker. Importantly, high levels of FASN were significantly negatively correlated with tumor immune infiltration in 35 different cancers. Additionally, FASN was significantly associated with tumor mutational burden (TMB) and microsatellite instability (MSI) in multiple malignancies, suggesting that it may be essential for tumor immunity. We also investigated the effects of FASN expression on immunotherapy efficacy and prognosis. In up to 15 tumors, it was significantly negatively correlated with immunotherapy-related genes, such as PD-1, PD-L1, and CTLA-4. Moreover, we found that tumors with high FASN expression may be more sensitive to immunotherapy and have a good prognosis with PD-L1 treatment. Finally, we confirmed the tumor-suppressive effect of mir-195-5p through FASN. Altogether, our results suggested that FASN may serve as a novel prognostic indicator and immunotherapeutic target in various malignancies.

Identification of multiple influential spreaders on networks by percolation under the SIR model.

Identification of multiple influential spreaders on complex networks is of great significance, which can help us speed up information diffusion and prevent disease from spreading to some extent. The traditional top-k strategy to solve an influence maximization problem based on node centrality is unsuitable for selecting several spreaders simultaneously because of influence overlapping. Besides, other heuristic methods have a poor ability to keep the balance between efficiency and computing time. In this paper, an efficient method is proposed to identify the decentralized influential spreaders on networks by edge percolation under the Susceptible-Infected-Recovered (SIR) model. Thanks to the average size of the connected component where one node is located under the edge percolation equivalent to the final spread range of this node under the SIR model approximately, it inspires us to choose suitable spreaders maximize the spread of influence. The experimental results show that our method has high efficiency compared with other benchmark methods on three synthetic networks and six empirical networks, and it also requires less time and cost.

Event detection in temporal social networks using a higher-order network model.

Event detection is one of the most important areas of complex network research. It aims to identify abnormal points in time corresponding to social events. Traditional methods of event detection, based on first-order network models, are poor at describing the multivariate sequential interactions of components in complex systems and at accurately identifying anomalies in temporal social networks. In this article, we propose two valid approaches, based on a higher-order network model, namely, the recovery higher-order network algorithm and the innovation higher-order network algorithm, to help with event detection in temporal social networks. Given binary sequential data, we take advantage of chronological order to recover the multivariate sequential data first. Meanwhile, we develop new multivariate sequential data using logical sequence. Through the efficient modeling of multivariate sequential data using a higher-order network model, some common multivariate interaction patterns are obtained, which are used to determine the anomaly degree of a social event. Experiments in temporal social networks demonstrate the significant performance of our methods finally. We believe that our methods could provide a new perspective on the interplay between event detection and the application of higher-order network models to temporal networks.

Bone Marrow Edema Syndrome of the Foot Treated with Extracorporeal Shock Wave Therapy: A Retrospective Case Series.

To determine the validity and safety of extracorporeal shock wave therapy (ESWT) in the treatment of bone marrow edema syndrome (BMES) of the foot. Twenty patients diagnosed as foot BMES in our Center were followed and treated by ESWT for 1 to 2 courses. The target of the ESWT treatment was the most obvious foot tenderness, or the most obvious part of bone edema on magnetic resonance imaging (MRI). One course of ESWT was 1 time/week, 5 times in total, with the shock wave energy flow density 0.18 mJ/mm2. The visual analog scale (VAS) and the American Orthopedic Foot and Ankle Society (AOFAS) scores of the foot were recorded before treatment, at 3 months after treatment and the last follow-up; the areas of BME before treatment and at the last follow-up were measured by the fat suppression MRI. Complications during treatment were also recorded. Twenty follow-up patients were obtained. Compared with the pretreatment, the patients had significant improvement in various indicators at 3 months after treatment (p < 0.01). The sagittal MRI at the last follow-up showed that the BME area decreased significantly (p < 0.01). Two patients developed transient erythema on their skin after treatment and alleviated after 2 days of rest. No serious complications were found during treatment. Our findings show that for patients with foot BMES, the use of ESWT treatment can effectively relieve local pain, improve the motor function of the foot and ankle. Two courses of treatment may be required for some patients.

MiR-200a and miR-200b restrain inflammation by targeting ORMDL3 to regulate the ERK/MMP-9 pathway in asthma.

BACKGROUND: Asthma is one of the most frequent and serious diseases worldwide. Inflammation has been reported to correlate with airway remodeling, which is critical for the progression of asthma. Better understanding of novel molecules modulating asthma and the underlying mechanism will benefit explorations of new treatments. Method: To explore the role of miR-200a and miR-200b in asthma, miR-200a mimics/inhibitor and miR-200b mimics/inhibitor were employed in A549 cells, respectively. Expression levels of inflammatory cytokines, including TNF-α, IL-4, IL-5, IL-13 and IL-1ß, were measured by quantitative real time polymerase chain reaction (qRT-PCR) and enzyme-linked immunosorbent assay (ELISA). A dual luciferase reporter assay was performed to identify whether miR-200a/200b directly bound to Orosomucoid 1-like 3 (ORMDL3). ERK, p-ERK and MMP-9, involved in downstream pathways of ORMDL3, were detected using qRT-PCR and western blotting. Results: MiR-200a/200b silencing significantly increased the expression of inflammatory cytokines, including TNF-α, IL-4, IL-5, IL-13 and IL-1ß, in A549 cells. ORMDL3 was the target gene of miR-200a/200b, with high expression levels in miR-200a inhibitor and miR-200b inhibitor groups. MiR-200a and miR-200b played synergistic roles in the regulation of the inflammatory effect in A549 cells. Expression levels of p-ERK and MMP-9 were significantly increased in miR-200a inhibitor and miR-200b inhibitor groups and were rescued by ERK inhibitor and MMP-9 inhibitor, respectively. Conclusion: These findings suggest that miR-200a and miR-200b are required to regulate asthma inflammation. Reduction in miR-200a/200b promotes the development of asthma inflammation by targeting ORMDL3 to activate the ERK/MMP-9 pathway. Therefore, elevating miR-200a and miR-200b and decreasing ORMDL3 might be potential strategies for inhibition of the asthma process.

Dynamic evolutionary metamodel analysis of the vulnerability of complex systems.

Because the collapse of complex systems can have severe consequences, vulnerability is often seen as the core problem of complex systems. Multilayer networks are powerful tools to analyze complex systems, but complex networks may not be the best choice to mimic subsystems. In this work, a cellular graph (CG) model is proposed within the framework of multilayer networks to analyze the vulnerability of complex systems. Specifically, cellular automata are considered the vertices of a dynamic graph-based model at the microlevel, and their links are modeled by graph edges governed by a stochastic model at the macrolevel. A Markov chain is introduced to illustrate the evolution of the graph-based model and to obtain the details of the vulnerability evolution with low-cost inferences. This CG model is proven to describe complex systems precisely. The CG model is implemented with two actual organizational systems, which are used on behalf of the typical flat structure and the typical pyramid structure, respectively. The computational results show that the pyramid structure is initially more robust, while the flat structure eventually outperforms it when being exposed to multiple-rounds strike. Finally, the sensitivity analysis results verify and strengthen the reliability of the conclusions.

Arthroscopic Ankle Arthrodesis for End-Stage Tuberculosis of the Ankle: A 2-Year Follow-Up.

Surgical treatment for end-stage ankle joint tuberculosis (TB) has rarely been reported. This study followed cases treated by arthroscopic arthrodesis for ankle joint TB to evaluate its efficacy and safety in the clinic. Patients who underwent arthroscopic ankle arthrodesis for ankle joint TB between April 11, 2010, and December 31, 2016, were followed. Their diagnoses were confirmed by bacterial culture or pathological examination. During arthroscopy, tissue samples were first obtained to further confirm the diagnosis. Then the necrotic tissue, hyperplasia of synovial tissue, and exfoliated cartilage were removed. Ankle joint arthrodesis was performed if the area of articular cartilage damage was >2 cm2. Continued nutritional support and standardized anti-TB drug treatment were given after surgery. Follow-up measurements included visual analogue scale score, American Orthopaedic Foot and Ankle Society score, erythrocyte sedimentation rate, and radiographic imaging. All 9 patients in this study, with an average age of 54 (range 37 to 68) years, were followed. The mean follow-up duration was 55.44 ± 31.15 (range 24 to 96) months. There were significant differences in the visual analogue scale scores, American Orthopaedic Foot and Ankle Society scores, and erythrocyte sedimentation rate between before treatment and 18 months postoperatively (p < .05). All patients (100%) showed union at 18 ± 4 weeks. Arthroscopic treatment for ankle joint TB has the advantages of minor trauma and low complications. It can be used to accurately obtain samples from specific areas of TB for further diagnosis. According to the degree of articular cartilage damage, the surgeon can determine whether to perform arthrodesis. Thorough debridement of necrotic tissue and residual articular cartilage on the fusion surface can improve the rate of ankle fusion.

Extracorporeal Shock Wave Therapy for Pain Relief After Arthroscopic Treatment of Osteochondral Lesions of Talus.

Arthroscopic treatment is an effective technique for osteochondral lesion of talus (OLT); however, some patients still suffer pain and limitation of activities after surgery. The purpose of this study was to evaluate the efficacy of extracorporeal shock wave therapy (ESWT) after ankle arthroscopy for OLT. We reviewed the clinical history of a series of 78 patients with OLT who underwent arthroscopic microfracture. ESWT was prescribed for 15 patients who complained of ankle pain and restriction of weightbearing activities 3 months postoperatively. The parameters assessed were visual analog scale (VAS) and American Orthopaedic Foot and Ankle Society (AOFAS) ankle-hindfoot scale scores (before ESWT, at 6 and 12 weeks, and at last follow-up after ESWT) and magnetic resonance imaging (MRI) before and 1 year after ESWT. Follow-up was 27.8 ± 15.2 months. VAS and AOFAS scores showed a significant improvement at 12 weeks after ESWT and a progressive trend at last follow-up. Areas of lesions in sagittal plane in MRI were distinctly reduced at last follow-up. ESWT for osteochondral lesions of talus after arthroscopy results in good clinical outcomes.

Rapidly Tuning the PID Controller Based on the Regional Surrogate Model Technique in the UAV Formation.

The leader-follower structure is widely used in unmanned aerial vehicle formation. This paper adopts the proportional-integral-derivative (PID) and the linear quadratic regulator controllers to construct the leader-follower formation. Tuning the PID controllers is generally empirical; hence, various surrogate models have been introduced to identify more refined parameters with relatively lower cost. However, the construction of surrogate models faces the problem that the singular points may affect the accuracy, such that the global surrogate models may be invalid. Thus, to tune controllers quickly and accurately, the regional surrogate model technique (RSMT), based on analyzing the regional information entropy, is proposed. The proposed RSMT cooperates only with the successful samples to mitigate the effect of singular points along with a classifier screening failed samples. Implementing the RSMT with various kinds of surrogate models, this study evaluates the Pareto fronts of the original simulation model and the RSMT to compare their effectiveness. The results show that the RSMT can accurately reconstruct the simulation model. Compared with the global surrogate models, the RSMT reduces the run time of tuning PID controllers by one order of magnitude, and it improves the accuracy of surrogate models by dozens of orders of magnitude.

Arthroscopically Assisted Anterior Treatment of Symptomatic Large Talar Bone Cyst.

Symptomatic cystic lesions of the talus are rare. The traditional operations usually do not provide visualization to reveal the deep structure of the lesion and could cause cartilage damage or other severe traumatic injury. We report an operative technique to reach the cystic lesion without talar cartilage damage, remove the lesion, and fill defect with a bone graft assisted by anterior arthroscopy and evaluate its safety and reliability for future study. Seven cases of talar bone cyst were included. The patients were placed in the supine position after anesthesia induction and noninvasive ankle traction was applied. Standard anteromedial and anterolateral portals were established to observe the ankle; the distal end of the medial approach was moderately enlarged to 2 to 3 cm. The biopsy specimen of the cyst was obtained under arthroscopic guidance; the cyst wall was abraded and the sclerotic rim drilled. Arthrocare radiofrequency ablation was performed to prevent recurrence. The defect was tightly impacted with autologous or allograft cancellous bone. All cysts in these cases were located in the medial talus; anteroposterior radiographs and computed tomographic coronary scan showed a cyst diameter of >1 cm. Intraoperative inspection showed a tiny chondral gap on the talar dome in 1 case and on the medial wall of talus in 1 case; no cartilage injury was found in the remainder. Two cases were impacted with grafted autogenous iliac bone into the talar defect and 5 cases with allograft cancellous bone. Computed tomography confirmed that the cysts had healed, with no signs of recurrence found in any patient at 1 year postoperatively. The mean American Orthopaedic Foot and Ankle Society ankle-hindfoot scale score increased from 65 preoperatively to 91 points postoperatively, a statistically significant difference (p < .01). No complications developed and no reoperations were required postoperatively. Arthroscopically assisted anterior treatment with autologous or allograft bone graft is an effective method for symptomatic large talar bone cysts.

Information Transfer Among the Components in Multi-Dimensional Complex Dynamical Systems.

In this paper, a rigorous formalism of information transfer within a multi-dimensional deterministic dynamic system is established for both continuous flows and discrete mappings. The underlying mechanism is derived from entropy change and transfer during the evolutions of multiple components. While this work is mainly focused on three-dimensional systems, the analysis of information transfer among state variables can be generalized to high-dimensional systems. Explicit formulas are given and verified in the classical Lorenz and Chua's systems. The uncertainty of information transfer is quantified for all variables, with which a dynamic sensitivity analysis could be performed statistically as an additional benefit. The generalized formalisms can be applied to study dynamical behaviors as well as asymptotic dynamics of the system. The simulation results can help to reveal some underlying information for understanding the system better, which can be used for prediction and control in many diverse fields.