**1. Introduction**

Numerous phenomena have been comprehended by studying the complex behaviors in many natural and non-natural dynamical systems. Understanding the chaotic behavior, which is a kind of nonlinear complex dynamical behavior, has provided a significant description of these systems. Although dynamical systems with chaotic behaviors are deterministic, long-term prediction of their behaviors is impossible [1]. Moreover, the sensitivity, topological mixing, and orbits density are the main characteristics of the chaotic systems [2–4]. Therefore, chaotic systems have valuable applications in various fields including computer science, telecommunication, physics, engineering, etc. [5–10]. In particular, due to the similarity between the characteristics of chaotic systems and the diffusion and confusion properties of cryptography [11], a wide body of chaos-based cryptographic applications has been presented in the last few years [12–17].

For the time being, discrete-time systems and continuous-time systems are the major types of chaotic systems. The former type is described by a difference equation, and it can be implemented through an iterative procedure, while the latter one is usually represented by a partial and/or ordinary differential equation. Edward Lorenz was the first to present a chaotic system with continuoustime [18]. Subsequently, several well-known continuous-time chaotic and hyperchaotic systems have been proposed such as Rössler [19], Sprott [20], Chen [21], and Lü [22] systems. On the other hand, the Logistic map, which was presented by Robert May, is the first clear example of a discrete-time system with chaotic behavior [23]. Since then various discrete-time chaotic and hyperchaotic systems have been presented in the literature [24–28].

During the past recent years, significant efforts in the prediction of chaotic systems' behaviors have been devoted through determining their parameters [29], or estimating their states [30]. Predicting the behavior of a chaotic system can render chaos-based cryptosystem insecure [31]. This has raised the need for measuring the complexity of the employed chaotic systems [32,33]. Therefore, numerous algorithms have emerged to measure the complexity of the systems' time series such as Fuzzy Entropy [34], Modified Permutation-Entropy [35], and Sample Entropy [36].

Due to the performance drawbacks of many existing chaotic systems in some attributes, for instance, frail chaos (i.e., chaotic behavior appears only in insulated zones of the system' parameters), it motivated researchers to propose systems with robust chaos that can encourage chaos-based cryptographic applications. An example of such weakness is that through a slight perturbation to a single parameter, it could make the system collapse into a non-chaotic zone of the system [37].

Based on the aforementioned description, this paper proposes a new chaotic discrete-time system, called the 2D infinite-collapse-Sine model (2D-ICSM). The 2D-ICSM exhibits a wide hyperchaotic range, good ergodicity, high complexity, and sensitivity. Therefore, 2D-ICSM could be an ideal source for chaos-based cryptographic applications. The main contributions of this work are as follows.


This paper is organized as follows. Section 2 introduces the 2D-ICSM and studies the stability of its equilibria. In Section 3, we analyze the dynamics of the 2D-ICSM. Section 4 demonstrates the high sensitivity and randomness of the 2D-ICSM. Section 5 demonstrates the detailed complexity performance of the 2D-ICSM. In Section 6, we introduce the proposed secure communication system. Section 7 illustrates the implementation of the communication system. Conclusions are presented in Section 8.
