Analysis of electrostatic floating potential fluctuations associated with multiple anodic double layer revealed a complexity dynamic coexisting with chaotic behavior. These externally controllable nonequilibrium quasi-stationary multiple anodic double layers were created in a cold cathode dc discharge setup in front of an extra anode which was used to supplement additional ionization. Despite the fact that chaos and complexity dynamics are often defined with entirely different properties, this study provides scenarios under which both can exist simultaneously. A stable multiple double-layer structure consisting of four successive double layers, each with positive and negative charged particles arranged in opposite sheets, was created when the anode potential exceeds a certain threshold value for a minimum gas breakdown bias between cathode and ground. After the stable multiple double layers was created, it was further controlled externally by varying the cathode bias between minimum gas breakdown bias of − 335 V and − 610 V at a pressure of 0.3 mbar for studying its advanced stages. With increase in cathode bias, multiple anodic double-layer structure advances towards the anode surface with the collapse of innermost layer due to the arrival of more energetic electrons in the anode zone. This process results from the self-organization and re-organization of charged particles in each double layer mediated by energetic electrons. The process continued until all the double layers disappeared and only an intense anode glow remained at anode for higher values of cathode bias. The chaotic dynamics of the system was studied at every stage by analyzing the corresponding floating potential fluctuations using FFT, phase space trajectories and nonlinear technique such as Lyapunov exponent, time-delay reconstruction etc. The analysis revealed the onset of chaos beyond − 410 V was triggered by the collapse of double layers. Estimation of correlation dimension, autocorrelation function and Hurst exponent unfolded the complexity features such as self-similarity and longtime dependence in the fluctuations. The value of correlation dimension reaches the maximum with an increase in cathode bias. Estimation of Hurst exponent using rescaled range analysis technique with values of H between 0.5 and 1 and algebraic decay of autocorrelation function provide signatures of long-range temporal correlations in the chaotic fluctuations and underlines the coexistence of complexity behavior.

对与多个阳极双层相关的静电浮置电位波动的分析揭示了与混沌行为共存的复杂性。这些外部可控的非平衡准静态多层阳极双层是在额外的阳极前面的冷阴极dc放电装置中创建的，该阳极用于补充额外的电离。尽管通常用完全不同的属性来定义混乱和复杂性动力学，但本研究提供了可以同时存在的场景。一种稳定的多层双层结构，由四个连续的双层组成，每个双层中的正负带电粒子排列在相对的片中，当阳极电势超过某个阈值以使阴极和地面之间的最小气体击穿偏置电压产生时，就会产生这种电流。创建稳定的多层双层后，可以通过在0.3 mbar的压力下-335 V和-610 V的最小气体击穿偏压之间改变阴极偏压来进一步对其进行外部控制，以研究其先进工艺。随着阴极偏压的增加，由于更多的高能电子到达阳极区，多个阳极双层结构朝着阳极表面前进，随着最内层的塌陷。该过程是由高能电子介导的每个双层中带电粒子的自组织和重新组织导致的。该过程一直持续到所有双层都消失并且对于较高的阴极偏压值，只有强烈的阳极辉光保留在阳极处。通过使用FFT，相空间轨迹和非线性技术（例如Lyapunov指数，时延重建等）分析相应的浮动电位波动，研究了系统的各个阶段的混沌动力学。分析表明，-410 V以上的混沌开始由双层倒塌触发。相关维数，自相关函数和Hurst指数的估计揭示了波动中的复杂性特征，例如自相似性和长期依赖性。随着阴极偏压的增加，相关尺寸的值达到最大值。