The dynamic characteristics of nonlinear circuits can be significantly enriched by the introduction of memristors. However, most existing memristor-based nonlinear circuits rely on inductive components, which limit the potential of memristor-based nonlinear circuits for miniaturization and on-chip implementation. Therefore, a memristor-based nonlinear circuit without inductor can overcome these limitations. In this work, a dual-memristor nonlinear circuit without inductor is designed, and then the dynamical equation of the dual-memristor nonlinear circuit and the corresponding energy function are obtained by using Kirchhoff's laws and Helmholtz's theorems. Furthermore, a novel hyperchaotic map is established from the dynamical equations of the dual-memristor nonlinear circuit by linearly transforming the state equations. Phase portraits, complexity measures, Lyapunov exponents, and bifurcation diagrams are employed to comprehensively analyze the complex dynamical behaviors of the proposed map. The results demonstrate that the map exhibits rich dynamical phenomena, such as periodic, chaotic, and hyperchaotic regimes. This work offers a valuable framework for applications in secure communication and pseudo-random number generation that require complex, high-dimensional chaotic dynamics. In addition, the elimination of the inductor not only makes the circuit model more amenable to very large-scale integration implementation but also provides a new and efficient discrete-time model for theoretical research in hyperchaos.
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