Nonreversible homoclinic snaking

Homoclinic snaking refers to the sinusoidal ‘snaking’ continuation curve of homoclinic orbits near a heteroclinic cycle connecting an equilibrium E and a periodic orbit P. Along this curve the homoclinic orbit performs more windings about the periodic orbit. Typically, this behaviour appears in reversible Hamiltonian systems. Here we discuss this phenomenon in systems without any particular structure. We give a rigorous analytical verification of homoclinic snaking under certain assumptions on the behaviour of the stable and unstable manifolds of E and P. We show how the snaking behaviour depends on the signs of the Floquet multipliers of P. Further we present a nonsnaking scenario. Finally, we show numerically that these assumptions are fulfilled in a model equation.     

Sequential dynamics of master–slave systems

Following on previous work, we discuss a scenario in which two neural ensembles have a master–slave arrangement. We will consider a more particular case in which the master system exhibits transient dynamics due to a stable heteroclinic sequence (SHS) and the slave system has attractors in the form of limit cycles. We will give sufficient conditions that guarantee the existence of a SHS in the form of a tube in the full phase space, together with an open stable heteroclinic channel that surrounds it. We present a numerical observation of chaotic-like transient behaviour different from well-known transient chaos.     

Switching near a network of rotating nodes

We study the dynamics of a Z ₂ ⊕ Z ₂-equivariant vector field in the neighbourhood of a heteroclinic network with a periodic trajectory and symmetric equilibria. We assume that around each equilibrium the linearization of the vector field has non-real eigenvalues. Trajectories starting near each node of the network turn around in space either following the periodic trajectory or due to the complex eigenvalues near the equilibria. Thus, in a network with rotating nodes, the rotations combine with transverse intersections of two-dimensional invariant manifolds to create switching near the network; close to the network, there are trajectories that visit neighbourhoods of the saddles following all the heteroclinic connections of the network in any given order. Our results are motivated by an example where switching was observed numerically by forced symmetry breaking of an asymptotically stable network with O(2) symmetry.     

Chaotic double cycling

We study the dynamics of a generic vector field in the neighbourhood of a heteroclinic cycle of non-trivial periodic solutions whose invariant manifolds meet transversely. The main result is the existence of chaotic double cycling: there are trajectories that follow the cycle making any prescribed number of turns near the periodic solutions, for any given bi-infinite sequence of turns. Using symbolic dynamics, arbitrarily close to the cycle, we find a robust and transitive set of initial conditions whose trajectories follow the cycle for all time and that is conjugate to a Markov shift over a finite alphabet. This conjugacy allows us to prove the existence of infinitely many heteroclinic and homoclinic subsidiary connections, which give rise to a heteroclinic network with infinitely many cycles and chaotic dynamics near them, exhibiting themselves switching and cycling. We construct an example of a vector field with Z ₃ symmetry in a five-dimensional sphere with a heteroclinic cycle having this property.     

Dynamics near the product of planar heteroclinic attractors

Motivated by problems in equivariant dynamics and connection selection in heteroclinic networks, Ashwin and Field investigated the product of planar dynamics where at least one of the factors was a planar homoclinic attractor. However, they were only able to obtain partial results in the case of a product of two planar homoclinic attractors. We give general results for the product of planar homoclinic and heteroclinic attractors. We show that the likely limit set of the basin of attraction of the product of two planar heteroclinic attractors is always the unique one-dimensional heteroclinic network which covers the heteroclinic attractors in the factors. The method we use is general and likely to apply to products of higher dimensional heteroclinic attractors as well as to situations where the product structure is broken but the cycles are preserved.     

Partial classification of heteroclinic behaviour associated with the perturbation of hexagonal planforms

Physical systems often exhibit pattern-forming instabilities. Equivariant bifurcation theory is often used to investigate the existence and stability of spatially doubly periodic solutions with respect to the hexagonal lattice. Previous studies have focused on the six- and twelve-dimensional representation of the hexagonal lattice where the symmetry of the model is perfect. Here, perturbation of group orbits of translation-free axial planforms in the six- and twelve-dimensional representations is considered. This problem is studied via the abstract action of the symmetry group of the perturbation on the group orbit of the planform. A partial classification for the behaviour of the group orbits is obtained, showing the existence of homoclinic and heteroclinic cycles between equilibria.     

余维4的Duffing-Van der Pol方程全局分岔分析

本文采用级数展开形式的Melnikov函数解决高余维分岔问题。通过研究一类5次项和3次项共存,具有异宿轨的Duffing-Van der Pol方程的余维4全局分岔问题,得到了该系统的分岔方程及全局拓扑结构,说明了该方法的可行性。研究结果表明,该系统有单个极限环、单个异宿轨、异宿轨和极限环共存、两个极限环共存等情况。最后通过数值模拟验正了理论分析结果的正确性。     

基于Melnikov方法的分数阶Duffing振子混沌阈值解析研究

研究了含有分数阶微分项的Duffing振子的分岔与混沌行为,利用等效刚度和等效阻尼的概念对分数阶微分项进行处理,将分数阶微分项等效成三角函数与指数函数的形式,用Melnikov方法分析了分数阶Duffing振子产生分岔与混沌的必要条件,得到了其解析结果.进行了解析解和数值解的比较,证明了解析结果的精确度,并通过仿真计算...     

非晶Mg65-xNi21Pr14Agx合金电极的制备及其放电性能

用铜模喷铸法制备了非晶Mg65-x Ni21-Pr14Ag x合金,采用球磨方法细化了合金颗粒。系统研究了不同Ag含量对非晶合金电极充放电行为、放电容量、循环稳定性、高倍率放电等性能的影响规律。结果表明,Ag元素的添加改善了合金电极充/放电性能,随着Ag含量的增加,非晶合金电极的最大放电容量和循环稳定性均呈现先增大后减小的规律,其高倍率放电性能也有所提高,适量Ag的添加可明显改善非晶MgNi-Pr系合金的放电性能。     

蓄能采暖地板用相变材料TH29热特性的实验研究

在地板采暖中使用相变蓄能材料不仅可以实现舒适供热的要求，还可以很好的起到节能和调节能量分配的作用。对一种符合地板采暖的水合盐类相变材料TH29的热特性进行实验研究，测试TH29的蓄放热特性、循环熔冻的热稳定性；分析了自然冷却与受迫冷却两种冷却凝固方式下的材料温度的变化曲线、材料中不同位置处相变过程的滞后现象；实验结果得出，在本实验条件下，TH29经相当数量的溶化与凝固循环后，相变的可逆性较好，可以保持热特性的稳定。     

循环网络模拟技术在土石方工程中的应用

土石方工程由于施工过程的复杂及受到众多随机因素的影响,很难用人工方法精确计算各道路的行车及排队情况,确定各道路的等级以及施工机械设备的数量。采用循环网络模拟技术,用挖、装、运、卸等仿真节点来模拟实际施工的相应过程,建立能反映土石方实际开挖过程的仿真模型。仿真得出的一系列施工参数为辅助管理人员做出决策提供参考依据。某工程中的成功应用表明,此方法快捷、便利,值得深入研究并推广应用。     

化成工艺对磷酸铁锂锂离子电池性能的影响

采用磷酸铁锂—石墨作为正负极材料制备超大容量叠片式单体电池(200Ah),分析两种不同化成工艺对锂离子电池性能的影响。分析了不同化成工艺后对应的电池负极的表面情况、电池内阻大小以及单体电池放电容量和循环性能等。结果显示,适当降低充电电压,有利于负极表面SEI膜的形成,并且形成的负极极片表面光滑,制备的电池具有更好的化成性能和循环性能。     

Rational synthesis of carbon shell coated polyaniline/MoS<Subscript>2</Subscript> monolayer composites for high-performance supercapacitors

Conducting polymers generally show high specific capacitance but suffer from poor rate capability and rapid capacitance decay, which greatly limits their practical applications in supercapacitor electrodes. To this end, many studies have focused on improving the overall capacitive performance by synthesizing nanostructured conducting polymers or by depositing a range of coatings to increase the active surface area exposed to the electrolyte and enhance the charge transport efficiency and structural stability. Despite this, simultaneously achieving high specific capacitance, good rate performance, and long cycle life remains a considerable challenge. Among the various two-dimensional (2D) layered materials, octahedral (1T) phase molybdenum disulfide (MoS₂) nanosheets have high electrical conductivity, large specific surface areas, and unique surface chemical characteristics, making them an interesting substrate for the controlled growth of nanostructured conducting polymers. This paper reports the rational synthesis of carbon shell-coated polyaniline (PANI) grown on 1T MoS₂ monolayers (MoS₂/PANI@C). The composite electrode comprised of MoS₂/PANI@C with a ~3 nm carbon shell exhibited a remarkable specific capacitance of up to 678 F·g^–1 (1 mV·s^–1), superior capacity retention of 80% after 10,000 cycles and good rate performance (81% at 10 mV·s^–1) due to the multiple synergic effects between the PANI nanostructure and 1T MoS₂ substrates as well as protection by the uniform thin carbon shell. These properties are comparable to the best overall capacitive performance achieved for conducting polymers-based supercapacitor electrodes reported thus far.

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聚乙烯醇和聚丙烯酸钠复合纳米纤维膜吸湿材料研究

本文通过纳米纺丝法制备了一类新型聚乙烯醇(PVA)与聚丙烯酸钠(PAAS)的复合纳米纤维膜吸湿材料(NFMs),并对该类材料进行性能测试和吸附模型验证,与通过溶液蒸发法制备的普通膜(SCMs)进行性能对比。结果表明:在25℃、相对湿度为80%下,PAAS质量分数为20%的PVA-PAAS复合纳米纤维膜最大吸附量为0.3 kg/kg,相比纯PVA纳米纤维膜吸附剂提高78%。在复合纳米纤维膜中,约90%的水蒸气吸附在5 min内完成,仅需15 min就能达到最大平衡吸附量。PVA-PAAS纳米纤维膜具有较快的脱附速率,在15 min内达到最大脱附量平衡点,是PVA-PAAS普通膜达到平衡所需时间的1/200。当再生空气状态为45℃、4 MPa和50℃、6 MPa时,吸附的水蒸气量脱除比率均高于80%。由此可见,PVA-PAAS纳米纤维膜能够在低温条件下较好地实现再生,可以利用太阳能等低品位能源。10次循环后,纳米纤维膜的吸附与脱附量、吸附与脱附速率均未发生变化,具有较好的稳定性。     

镍氢电池负极材料V2Ti0.5Cr0.5Ni1-xMox(x=0.02~0.08)的结构和电化学性能

为了改善镍氢电池负极材料的循环稳定性能, 采用真空感应电弧熔炼炉制备了V₂Ti_0.5Cr_0.5Ni_1-xMo_x (x=0.02~0.08)合金, 分析了不同含量的Mo替代Ni之后对合金电极的组织结构及电化学性能的影响。研究结果表明, 电极材料主要由BCC结构的V基固溶体主相和TiNi二次相组成, 随着合金中Mo替代Ni含量x由0.02增加到0.08, 合金电极的放电容量先增加后降低, 合金电极的循环稳定性能以及电化学动力学性能先得到改善而后降低, 合金电极的综合性能均在x=0.04时达到最好。     

动力学系统的稳定性与非线性行为的一种分析计算方法

在非线性动力学系统中,分析系统参数的变化对系统稳定性影响和在系统不稳定的情况下系统参数对振动幅值的影响是十分重要的两个方面。针对常见的非线性动力学模型,提出了一个利用特征根判别、规范形计算等方法对系统非线性特性和稳定性进行分析计算的方法。应用该方法进行计算分析的实例说明该方法十分有效。