Ultra-low-voltage sinh-domain implementation of delayed inertial neuron is introduced in this paper. The complex dynamical behavior of the neuron has been verified using three different activation functions, namely tanh, unipolar sigmoidal and bipolar sigmoidal. The networks containing two and four neurons have been designed, and their complex dynamical behavior has also been verified. The proposed implementation vis-à -vis the already reported designs offers the benefits of: (1) low-voltage operation, (2) integrability, due to resistor-less design and the employment of only grounded components, (3) electronic tunability of performance parameters by external currents, which adds flexibility to the proposed designs even after their final fabrication, (4) absence of inductors as, in contrast to reported designs, the delay has been implemented using component substitution method where inductors have been replaced by emulated inductors and (5) low-power implementation due to the inherent class AB nature of sinh-domain technique. Besides, for the first time, the complex dynamical behavior of four-neuron delayed inertial network has been implemented and its functioning for different activations functions has been considered and verified. HSPICE simulator tool and TSMC 130 nm CMOS process were used to evaluate and verify the correct functioning of the model. © 2019, Springer-Verlag London Ltd., part of Springer Nature.