This paper studies a four-dimensional (4D) memristive system modified from the 3D chaotic system proposed by Lü and Chen. The new system keeps the symmetry and dissipativity of the original system and has an uncountable infinite number of stable and unstable equilibria. By varying the strength of the memristor, we find rich complex dynamics, such as limit cycles, torus, chaos, and hyperchaos, which can peacefully coexist with the stable equilibria. To explain such coexistence, we compute the unstable manifolds of the equilibria, find that the manifolds create a safe zone for the hyperchaotic attractor, and also find many heteroclinic orbits. To verify the existence of hyperchaos in the 4D memristive circuit, we carry out a computerassisted proof via a topological horseshoe with twodirectional expansions, as well as a circuit experiment on oscilloscope views.

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So far, plenty of microwave power circuits such as microwave diode rectifiers are mainly designed and analyzed by conventional electromagnetic (EM) co-simulation method based on the semiconductor equivalent circuit models. However, the simplified equivalent circuit model may contribute to loss of precision at high frequencies or under high power. Compared with the equivalent circuit model, the semiconductor physical model provides a means for studying the physics of electron transport, and thus, better describes the semiconductor device. This paper explores analyzing microwave diode rectifiers by employing a physical model-based field-circuit co-simulation method. This method combines the physical model-based circuit simulation to the finite-difference time-domain (FDTD)-based field-circuit co-simulation and thus, achieves accurate and effective hybrid full-wave field-circuit co-simulation. For validation, two diode rectifiers working at S-and C-band, respectively, are simulated and analyzed by the proposed method. The simulation result agrees well with measurement and shows higher accuracy than the equivalent circuit model-based simulation.INDEX TERMS Microwave rectifier, Schottky diode, physical model, filed-circuit co-simulation.