Unpredictable oscillations of SICNNs with delay

Replication of period-doubling route to chaos in impulsive systems

“…For different values of the parameter 𝜇, the logistic map (9) possesses various dynamical phenomena such as homoclinic and heteroclinic orbits, period-doubling cascades, intermittency, and chaos in the senses of Li-Yorke, Devaney and Poincaré [39]- [42]. The logistic map was used in [43] to examplify continuous unpredictable motions in shunting inhibitory cellular neural networks. Moreover, the reader is referred to [44] for discontinuous unpredictable motions generated by impulsive systems.…”

Generation of Synchronous Unpredictable Oscillations by Coupled Hopfield Neural Networks

“…The papers [8]- [10] are concerned with the existence, uniqueness and stability of unpredictable oscillations in systems of differential equations. The reader is referred to the papers [11,12] for unpredictable oscillations in shunting inhibitory cellular neural networks.…”

A Novel Criterion for Unpredictable Motions

“…Miller [5] generalized the notion of unpredictable points to the case of semiflows with arbitrary acting abelian topological monoids, whereas Thakur and Das [6] demonstrated that at least one of the factors is Poincaré chaotic provided that the same is true for finite or countably infinite products of semiflows. Additionally, differential equations with hyperbolic linear parts exhibiting unpredictable solutions were studied in [8,9], and the existence of unpredictable outputs in cellular neural networks can be found in papers [10,11].…”