Using the discrete fractional calculus, a novel discrete fractional-order food chain model for the case of strong pressure on preys map is proposed. Dynamical behaviors of the model involving stability analysis of its equilibrium points, bifurcation diagrams and phase portraits are investigated. It is demonstrated that the model can exhibit a variety of dynamical behaviors including stable steady states, periodic and quasiperiodic dynamics. Then, a hybrid encryption scheme based on chaotic behavior of the model along with elliptic curve key exchange scheme is proposed for colored plain images. The hybrid scheme combines the characteristics of noise-like chaotic dynamics of the map, including high sensitivity to values of parameters, with the advantages of reliable elliptic curves-based encryption systems. Security analysis assures the efficiency of the proposed algorithm and validates its robustness and efficiency against possible types of attacks.

中文翻译：

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混沌离散分数阶食物链模型及混合图像加密方案应用

利用离散分数演算，提出了一种新的离散分数阶食物链模型。研究了该模型的动力学行为，包括其平衡点，分叉图和相像的稳定性分析。结果表明，该模型可以表现出多种动力学行为，包括稳定的稳态，周期性和准周期性动力学。然后，提出了一种基于模型混沌行为和椭圆曲线密钥交换方案的混合加密方案。混合方案结合了地图的类似噪声的混沌动力学特性，包括对参数值的高度敏感性，以及可靠的基于椭圆曲线的加密系统的优点。