This paper presents cryptanalysis methods for a class of chaos-based image encryption schemes with a permutation-diffusion architecture. Assuming that the permutation and diffusion session keys remain unchanged across all encryption and decryption rounds, the proposed chosen-plaintext and Chosen-Ciphertext Attacks (CCAs) exploit two properties of the diffusion equation. Under the Chosen-Plaintext Attack (CPA), the permutation key and the equivalent diffusion key are recovered for schemes with at most two encryption rounds. Under the CCA, the equivalent diffusion key is recovered for any number of decryption rounds, assuming that the permutation key has been recovered using Solak’s method. The proposed attacks are described step by step. Illustrative simulations demonstrate the key recovery process and the effectiveness of the proposed attacks and quantify the computational cost of the main recovery steps in diffusion-key recovery.
An asymmetric quintic van der Pol–Duffing–Helmholtz oscillator under harmonic forcing is analyzed using mean-corrected harmonic balance, basin computation, Poincaré shooting, Floquet multipliers and complementary chaos diagnostics. Because quadratic stiffness couples the zero Fourier mode to the fundamental, a zero-mean first-harmonic approximation is structurally inconsistent. The coupled mean–amplitude reduction is therefore benchmarked at several forcing levels against direct integration and against the conventional zero-mean truncation; higher-harmonic content is also reported to delimit its useful range. Here [Formula: see text] denotes the quadratic-stiffness asymmetry coefficient, [Formula: see text] the forcing frequency and [Formula: see text] the forcing amplitude. A symmetric [Formula: see text] reference isolates the equilibrium shift and stability asymmetry generated by the quadratic term. Basin fractions for coexisting period-1 and period-2 responses are checked under [Formula: see text]–[Formula: see text] grid refinement. At [Formula: see text], period-3 and period-6 branches undergo multiplier-confirmed flips near [Formula: see text] and [Formula: see text]. Their two-parameter continuation is extended substantially in frequency, with the period-3 curve developing a near-vertical turning region. Chaos is supported by converged positive largest Lyapunov exponents and an independent 0–1 test. Two Lyapunov atlases from distinct initial conditions quantify the basin dependence of the parameter-plane picture.
With the continuous advancement of remote sensing imaging technology, the resolution of images has significantly improved, and their applications have expanded to military reconnaissance, environmental monitoring, resource surveys, and other critical domains. Traditional encryption algorithms often suffer from high computational complexity, limited real-time performance, and inadequate resistance to attacks when encrypting large-sized, highly correlated remote sensing image data. To address these challenges, this paper proposes a highly secure image encryption algorithm based on a multifunctional neuron and a dynamic S-box mechanism. First, the pixel positions of the image are scrambled using a zigzag algorithm. Subsequently, chaotic sequences generated by the multifunctional neuron are employed to diffuse the pixel values. Furthermore, a dynamic S-box constructed from these chaotic sequences is applied to enhance the diffusion effect of the image pixels. The experimental results demonstrate that the proposed encryption scheme can effectively resist exhaustive, statistical, and differential attacks. This research will provide a theoretical framework and a research methodology for the secure transmission of remote sensing images.
In this paper, we develop convergent numerical schemes to approximate absolutely continuous invariant measures of piecewise convex maps with countably many branches, based on a modified piecewise-linear Markov method and a novel piecewise quadratic B-spline method. The proposed schemes are effective for studying piecewise convex chaotic maps. Notably, while it ensures the same convergence order as the piecewise-linear method, the piecewise quadratic B-spline method enhances the smoothness of the approximate density. Numerical examples demonstrate the efficacy of these approaches.
This paper focuses on analyzing the complex dynamical behaviors of a delayed Leslie-Gower system with double Allee effect, which encompasses both strong and weak Allee effects. First, the existence and boundedness of the equilibrium point of the model are analyzed, which guarantees the validity of the predator-prey model. Subsequently, the Hopf bifurcation dynamics is obtained in detail for various types of delay, and the property of the Bogdanov-Takens (B-T) bifurcation under multi-delay conditions is researched by the normal form theory and the central manifold theorem. Finally, numerical simulations are conducted to investigate the specific effects of delays and Allee effect, the numerical results are consistent with the theoretical analysis. Interestingly, the results of the thesis indicate that the richness of model dynamics can be achieved by adjusting bifurcation parameters and time delays, which play crucial roles in ecological conservation and quantity control.
