We consider the dynamical effects of electromagnetic flux on discrete Chialvo neuron model. It is shown that model can exhibit rich behaviors such as multistability, firing patterns, antimonotonicity, closed invariant curves, various routes to chaos, and fingered chaotic attractors. The system enters a chaos regime via period-doubling cascades, reverse route, curve chaos. results were confirmed using techniques bifurcation diagrams, Lyapunov exponent diagram, phase portraits, basins...

Abstract This contribution is devoted to the study of collective behavior two HR neurons followed by a network neurons. The coupled neuron was obtained from connection between traditional 3D and memristive 2D via gap junction. dynamical properties this first topology revealed that it dissipative therefore can support complex phenomena. From numerical simulations, found display variety behaviors just varying control parameter. Amongst these found, we have periodic bursting or spiking,...

In this study, we investigate the occurrence of a three-frequency quasi-periodic torus in three-dimensional Lotka–Volterra map. Our analysis extends to observation doubling bifurcation closed invariant curve, leading subsequent transition into state hyperchaos. The absorption various saddle periodic orbits hyperchaotic attractor is demonstrated through distance computation, and explore dimensionality both stable unstable manifolds. Various routes cyclic disjoint structures are presented....

The phenomenon of hidden heterogeneous extreme multistability is rarely reported in coupled neurons. This investigated this contribution using a model 2D FitzHugh-Nagumo neuron with 3D Hindmarsh-Rose through multistable memristive synapse. investigation the equilibria revealed that equilibrium free and, thus, displays dynamics. Some traditional nonlinear analysis tools are used to demonstrate system able exhibit coexistence an infinite number electrical activities involving both periodic and...

Abstract Similar to period-doubling bifurcation of fixed points, periodic orbits, it has been found since 1980's that a corresponding doubling can also be in the case quasiperiodic orbits. Doubling bifurcations orbits an important consequence on dynamics system under consideration. Recently, shown subsequent doublings closed invariant curves lead formation Shilnikov attractors. In this contribution, we illustrate for first time discrete neuron system, phenomenon curves. We show presence...

Abstract We perform a numerical study on the application of electromagnetic flux heterogeneous network Chialvo neurons represented by ring-star topology. Heterogeneities are realized introducing additive noise modulations both central–peripheral and peripheral–peripheral coupling links in topology not only varying space but also time. The variation time is understood two probabilities, one for connections other connections, respectively, that update with each iteration have further reported...

In this paper, we introduce a novel image encryption and decryption algorithm using hyperchaotic signals from the 3D map, 2D memristor Convolutional Neural Network (CNN), key sensitivity analysis to achieve robust security high efficiency. The starts with scrambling of gray images by map yield complex sequences under disruption pixel values; robustness original is further reinforced employing CNN learn intricate patterns add safety layer. shown analysis, i.e., average elements. other factors...

In this paper we have introduced and investigated the collective behavior of a network memristive Hindmarsh-Rose (HR) neurons. The proposed model was built considering autapse traditional 2D HR neuron. Using one-parameter bifurcation diagram its corresponding maximal Lyapunov exponent graph, showed that able to exhibit reverse period doubling route chaos, phenomenon interior exterior crises. Three different configurations ring-star neuron model, including ring-star, ring, star, been...

We study numerically the spatiotemporal dynamics in a ring network of nonlocally coupled nonlinear oscillators, each represented by two-dimensional discrete-time model classical van der Pol oscillator. It is shown that discretized oscillator exhibits richer behavior, combining peculiarities both original system and its own dynamics. Moreover, large variety structures observed discrete oscillators when discretization parameter coupling strength are varied. Regimes such as coexistence...

The study of billiards investigates the trajectories particles that move freely in a region and reflect elastically at boundaries. Although there is already considerable understanding about invariant spanning curves, also known as whispering gallery orbits context billiards, their determination phase space system, addition to analysis existence still an open question. Our proposal present numerical method based on Slater’s theorem, capable determining location these curves space, well...

<title>Abstract</title> We explore numerically the spatiotemporal dynamics of networks nonlocally coupled Rulkov maps (discrete-time neuron models) under Levy noise. show how network depends on control parameters individual elements, coupling parameters, and noise generators. reveal for first time analyze possibility observing coherence-resonance solitary states, state chimeras, phase chimeras. that changes in radius can influence number incoherence clusters Conversely, when strength is...

We present numerical results for the synchronization phenomena in a bilayer network of repulsively coupled 2D lattices van der Pol oscillators. consider cases when layers have either different or same types intra-layer coupling topology. When are uncoupled, lattice oscillators with repulsive interaction typically demonstrates labyrinth-like pattern, while attractively shows regular spiral wave structure. reveal first time that inter-layer leads to anti-phase spatiotemporal structures all...

We study numerically effects of time delay in networks delay-coupled excitable FitzHugh-Nagumo systems with dissipation. Generation periodic self-sustained oscillations and its threshold are analyzed depending on the dissipation a single neuron, time, random initial conditions. The peculiarities spatiotemporal dynamics time-delayed bidirectional ring-structured neuronal investigated cases local nonlocal coupling topology between nodes, first-order nonequilibrium phase transition to synchrony...

In this paper, we report the bifurcations of mode-locked periodic orbits occurring in maps three or higher dimensions. The “torus” is represented by a closed loop discrete time, which contains stable and unstable cycles same periodicity, manifolds saddle. We investigate two types “doubling” such loops: (a) disjoint loops are created iterates toggle between them, (b) length invariant curve doubled. Our work supports conjecture Gardini Sushko, says that type bifurcation depends on sign third...