How can the networks with various topologies change the occurrence of bifurcation points in a period-doubling route to chaos: a case study of neural networks in the presence and absence of disturbance

• Published in: European physical journal plus Vol. 138; no. 4; p. 362
• Main Authors: Navid Moghadam, Nastaran, Ramamoorthy, Ramesh, Nazarimehr, Fahimeh, Rajagopal, Karthikeyan, Jafari, Sajad
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 27.04.2023; Springer Nature B.V
• Subjects: Applied and Technical Physics; Atomic; Behavior; Bifurcations; Complex Systems; Condensed Matter Physics; Consciousness; Coupling; Mathematical and Computational Physics; Mathematical models; Molecular; Neural networks; Neurons; Nodes; Optical and Plasma Physics; Oscillators; Parameters; Period doubling; Physics; Physics and Astronomy; Recovery time; Regular Article; Theoretical; Topology
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/s13360-023-03939-w

Several mathematical models, such as Hodgkin–Huxley, FitzHugh–Nagumo, Morris–Lecar, Hindmarsh–Rose, and Leech, have been proposed to explain neural behaviors. Changing the parameters of neural models reveals the various neural dynamics. To make these models as realistic as possible, they should be studied in the networks, where there are interactions between the neurons. Hence, investigating neural models in the networks can be helpful. This study examines the attention-deficit disorder model's bifurcation points in both regular and irregular networks. The networks are analyzed in two cases. In the first case, networks are studied where perturbations enter one node. Calculating the recovery time of the disturbed neuron can investigate the bifurcation points. Results show that recovery time reveals the dynamical variation of the disturbed node. The second case examines networks with different coupling strengths and nodes' degrees. Results indicate that as coupling strengths and nodes' degree increase, bifurcations occur in the smaller parameters in the period-doubling route to chaos. A general trend cannot be seen in the inverse route of period doubling.