This work presents a general framework for developing a multiparameter 1-D chaotic system for uniform and robust chaotic operation across the parameter space. This is important for diverse practical applications where parameter disturbance may cause degradation or even complete disappearance of chaotic properties. The wide uninterrupted chaotic range and improved chaotic properties are demonstrated with the aid of stability analysis, bifurcation diagram, Lyapunov exponent (LE), Kolmogorov entropy, Shannon entropy, and correlation coefficient. We also demonstrate the proposed system's amenability to cascading for further performance improvement. We introduce an efficient field-programmable gate array-based implementation and validate its chaotic properties using comparison between simulation and experimental results. Cascaded normalized linearly-combined chaotic system (NLCS) exhibits average LE, chaotic ratio, and chaotic parameter space of 1.364, 100%, and $1.1\times 10^{12}$ , respectively, for 10-bit parameter values. We provide a thorough comparison of our system with prior works both in terms of performance and hardware cost. We also introduce a simple extension scheme to build 2-D robust, hyperchaotic NLCS maps. We present a novel reconfigurable multiparameter pseudorandom number generator and validate its randomness using two standard statistical tests, namely, National Institute of Standards and Technology SP 800-22 and FIPS PUB 140-2. Finally, we outline six potential applications where NLCS will be useful.

中文翻译：

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归一化线性组合混沌系统：设计、分析、实现和应用

这项工作提出了一个开发多参数一维混沌系统的通用框架，以便在参数空间上进行均匀且鲁棒的混沌操作。这对于参数扰动可能导致混沌特性退化甚至完全消失的各种实际应用非常重要。借助稳定性分析、分岔图、Lyapunov 指数 (LE)、Kolmogorov 熵、Shannon 熵和相关系数，证明了宽的不间断混沌范围和改进的混沌特性。我们还展示了所提出的系统对级联的适应性，以进一步提高性能。我们引入了一种基于现场可编程门阵列的高效实现，并通过仿真和实验结果之间的比较来验证其混沌特性。级联归一化线性组合混沌系统 (NLCS) 的平均 LE、混沌比和混沌参数空间分别为 1.364、100% 和$1.1\乘以10^{12}$ ，分别表示 10 位参数值。我们在性能和硬件成本方面对我们的系统与之前的工作进行了全面的比较。我们还引入了一个简单的扩展方案来构建二维鲁棒、超混沌 NLCS 地图。我们提出了一种新颖的可重构多参数伪随机数生成器，并使用两个标准统计测试（即美国国家标准与技术研究所 SP 800-22 和 FIPS PUB 140-2）验证其随机性。最后，我们概述了 NLCS 的六种潜在应用。