424 research outputs found
Exponential multistability of memristive Cohen-Grossberg neural networks with stochastic parameter perturbations
© 2020 Elsevier Ltd. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/.Due to instability being induced easily by parameter disturbances of network systems, this paper investigates the multistability of memristive Cohen-Grossberg neural networks (MCGNNs) under stochastic parameter perturbations. It is demonstrated that stable equilibrium points of MCGNNs can be flexibly located in the odd-sequence or even-sequence regions. Some sufficient conditions are derived to ensure the exponential multistability of MCGNNs under parameter perturbations. It is found that there exist at least (w+2) l (or (w+1) l) exponentially stable equilibrium points in the odd-sequence (or the even-sequence) regions. In the paper, two numerical examples are given to verify the correctness and effectiveness of the obtained results.Peer reviewe
Amplitude Death: The emergence of stationarity in coupled nonlinear systems
When nonlinear dynamical systems are coupled, depending on the intrinsic
dynamics and the manner in which the coupling is organized, a host of novel
phenomena can arise. In this context, an important emergent phenomenon is the
complete suppression of oscillations, formally termed amplitude death (AD).
Oscillations of the entire system cease as a consequence of the interaction,
leading to stationary behavior. The fixed points that the coupling stabilizes
can be the otherwise unstable fixed points of the uncoupled system or can
correspond to novel stationary points. Such behaviour is of relevance in areas
ranging from laser physics to the dynamics of biological systems. In this
review we discuss the characteristics of the different coupling strategies and
scenarios that lead to AD in a variety of different situations, and draw
attention to several open issues and challenging problems for further study.Comment: Physics Reports (2012
Nonlinearity of local dynamics promotes multi-chimeras
Chimera states are complex spatio-temporal patterns in which domains of
synchronous and asynchronous dynamics coexist in coupled systems of
oscillators. We examine how the character of the individual elements influences
chimera states by studying networks of nonlocally coupled Van der Pol
oscillators. Varying the bifurcation parameter of the Van der Pol system, we
can interpolate between regular sinusoidal and strongly nonlinear relaxation
oscillations, and demonstrate that more pronounced nonlinearity induces
multi-chimera states with multiple incoherent domains. We show that the
stability regimes for multi-chimera states and the mean phase velocity profiles
of the oscillators change significantly as the nonlinearity becomes stronger.
Furthermore, we reveal the influence of time delay on chimera patterns
Convergence of Neural Networks with a Class of Real Memristors with Rectifying Characteristics
The paper considers a neural network with a class of real extended memristors obtained via the parallel connection of an ideal memristor and a nonlinear resistor. The resistor has the same rectifying characteristic for the current as that used in relevant models in the literature to account for diode-like effects at the interface between the memristor metal and insulating material. The paper proves some fundamental results on the trajectory convergence of this class of real memristor neural networks under the assumption that the interconnection matrix satisfies some symmetry conditions. First of all, the paper shows that, while in the case of neural networks with ideal memristors, it is possible to explicitly find functions of the state variables that are invariants of motions, the same functions can be used as Lyapunov functions that decrease along the trajectories in the case of real memristors with rectifying characteristics. This fundamental property is then used to study convergence by means of a reduction-of-order technique in combination with a Lyapunov approach. The theoretical predictions are verified via numerical simulations, and the convergence results are illustrated via the applications of real memristor neural networks to the solution of some image processing tasks in real time
Persistent Entrainment in Non-linear Neural Networks With Memory
We investigate the dynamics of a non-linear network with noise, periodic forcing and delayed feedback. Our model reveals that there exist forcing regimes—called persistent entrainment regimes—in which the system displays oscillatory responses that outlast the termination of the forcing. Our analysis shows that in presence of delays, periodic forcing can selectively excite components of an infinite reservoir of intrinsic modes and hence display a wide range of damped frequencies. Mean-field and linear stability analysis allows a characterization of the magnitude and duration of these persistent oscillations, as well as their dependence on noise intensity and time delay. These results provide new perspectives on the control of non-linear delayed system using periodic forcing
Complex partial synchronization patterns in networks of delay-coupled neurons
We study the spatio-temporal dynamics of a multiplex network of delay-coupled FitzHugh–Nagumo oscillators with non-local and fractal connectivities. Apart from chimera states, a new regime of coexistence of slow and fast oscillations is found. An analytical explanation for the emergence of such coexisting partial synchronization patterns is given. Furthermore, we propose a control scheme for the number of fast and slow neurons in each layer.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept
Synchronous solutions and their stability in nonlocally coupled phase oscillators with propagation delays
We study the existence and stability of synchronous solutions in a continuum
field of non-locally coupled identical phase oscillators with
distance-dependent propagation delays. We present a comprehensive stability
diagram in the parameter space of the system. From the numerical results a
heuristic synchronization condition is suggested, and an analytic relation for
the marginal stability curve is obtained. We also provide an expression in the
form of a scaling relation that closely follows the marginal stability curve
over the complete range of the non-locality parameter.Comment: accepted in Phys. Rev. E (2010
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