1,375 research outputs found
Phase reduction approach to synchronization of spatiotemporal rhythms in reaction-diffusion systems
Reaction-diffusion systems can describe a wide class of rhythmic
spatiotemporal patterns observed in chemical and biological systems, such as
circulating pulses on a ring, oscillating spots, target waves, and rotating
spirals. These rhythmic dynamics can be considered limit cycles of
reaction-diffusion systems. However, the conventional phase-reduction theory,
which provides a simple unified framework for analyzing synchronization
properties of limit-cycle oscillators subjected to weak forcing, has mostly
been restricted to low-dimensional dynamical systems. Here, we develop a
phase-reduction theory for stable limit-cycle solutions of infinite-dimensional
reaction-diffusion systems. By generalizing the notion of isochrons to
functional space, the phase sensitivity function - a fundamental quantity for
phase reduction - is derived. For illustration, several rhythmic dynamics of
the FitzHugh-Nagumo model of excitable media are considered. Nontrivial phase
response properties and synchronization dynamics are revealed, reflecting their
complex spatiotemporal organization. Our theory will provide a general basis
for the analysis and control of spatiotemporal rhythms in various
reaction-diffusion systems.Comment: 19 pages, 6 figures, see the journal for a full versio
Diffusive Mobile Molecular Communications Over Time-Variant Channels
This letter introduces a formalism for modeling time-variant channels for
diffusive molecular communication systems. In particular, we consider a fluid
environment where one transmitter nano-machine and one receiver nano-machine
are subjected to Brownian motion in addition to the diffusive motion of the
information molecules used for communication. Due to the stochastic movements
of the transmitter and receiver nano-machines, the statistics of the channel
impulse response change over time. We show that the time-variant behaviour of
the channel can be accurately captured by appropriately modifying the diffusion
coefficient of the information molecules. Furthermore, we derive an analytical
expression for evaluation of the expected error probability of a simple
detector for the considered system. The accuracy of the proposed analytical
expression is verified via particle-based simulation of the Brownian motion.Comment: 4 pages, 3 figures, 1 table. Accepted for publication in IEEE
Communications Letters (Author's comment: Manuscript submitted Jan. 19, 2017;
revised Feb. 20, 2017; accepted Feb. 22, 2017
Bounds on Distance Estimation via Diffusive Molecular Communication
This paper studies distance estimation for diffusive molecular communication.
The Cramer-Rao lower bound on the variance of the distance estimation error is
derived. The lower bound is derived for a physically unbounded environment with
molecule degradation and steady uniform flow. The maximum likelihood distance
estimator is derived and its accuracy is shown via simulation to perform very
close to the Cramer-Rao lower bound. An existing protocol is shown to be
equivalent to the maximum likelihood distance estimator if only one observation
is made. Simulation results also show the accuracy of existing protocols with
respect to the Cramer-Rao lower bound.Comment: 7 pages, 5 figures, 1 table. Will be presented at the 2014 IEEE
Global Communications Conference (GLOBECOM) in Austin, TX, USA, on December
9, 201
Synchronization of reaction–diffusion Hopfield neural networks with s-delays through sliding mode control
Synchronization of reaction–diffusion Hopfield neural networks with s-delays via sliding mode control (SMC) is investigated in this paper. To begin with, the system is studied in an abstract Hilbert space C([–r; 0];U) rather than usual Euclid space Rn. Then we prove that the state vector of the drive system synchronizes to that of the response system on the switching surface, which relies on equivalent control. Furthermore, we prove that switching surface is the sliding mode area under SMC. Moreover, SMC controller can also force with any initial state to reach the switching surface within finite time, and the approximating time estimate is given explicitly. These criteria are easy to check and have less restrictions, so they can provide solid theoretical guidance for practical design in the future. Three different novel Lyapunov–Krasovskii functionals are used in corresponding proofs. Meanwhile, some inequalities such as Young inequality, Cauchy inequality, Poincaré inequality, Hanalay inequality are applied in these proofs. Finally, an example is given to illustrate the availability of our theoretical result, and the simulation is also carried out based on Runge–Kutta–Chebyshev method through Matlab
Exponential synchronization for reaction-diffusion neural networks with mixed time-varying delays via periodically intermittent control
This paper deals with the exponential synchronization problem for reaction-diffusion neural networks with mixed time-varying delays and stochastic disturbance. By using stochastic analysis approaches and constructing a novel Lyapunov–Krasovskii functional, a periodically intermittent controller is first proposed to guarantee the exponential synchronization of reaction-diffusion neural networks with mixed time-varying delays and stochastic disturbance in terms of p-norm. The obtained synchronization results are easy to check and improve upon the existing ones. Particularly, the traditional assumptions on control width and time-varying delays are removed in this paper. This paper also presents two illustrative examples and uses simulated results of these examples to show the feasibility and effectiveness of the proposed scheme
Diffusive Molecular Communications with Reactive Signaling
This paper focuses on molecular communication (MC) systems where the
signaling molecules may participate in a reversible bimolecular reaction in the
channel. The motivation for studying these MC systems is that they can realize
the concept of constructive and destructive signal superposition, which leads
to favorable properties such as inter-symbol interference (ISI) reduction and
avoiding environmental contamination due to continuous release of molecules
into the channel. This work first derives the maximum likelihood (ML) detector
for a binary MC system with reactive signaling molecules under the assumption
that the detector has perfect knowledge of the ISI. The performance of this
genie-aided ML detector yields an upper bound on the performance of any
practical detector. In addition, two suboptimal detectors of different
complexity are proposed. The proposed ML detector as well as one of the
suboptimal detectors require the channel response (CR) of the considered MC
system. Moreover, the CR is needed for the performance evaluation of all
proposed detectors. However, analyzing MC with reactive signaling is
challenging since the underlying partial differential equations that describe
the reaction-diffusion mechanism are coupled and non-linear. Therefore, an
algorithm is developed in this paper for efficient computation of the CR to any
arbitrary transmit symbol sequence. The accuracy of this algorithm is validated
via particle-based simulation. Simulation results using the developed CR
algorithm show that the performance of the proposed suboptimal detectors can
approach that of the genie- aided ML detector. Moreover, these results show
that MC systems with reactive signaling have superior performance relative to
those with non-reactive signaling due to the reduction of ISI enabled by the
chemical reactions.Comment: This paper has been submitted to IEEE International Conference on
Communications (ICC) 201
Distributed Parameter State Estimation for the Gray–Scott Reaction-Diffusion Model
A constructive approach is provided for the reconstruction of stationary and non-stationary patterns in the one-dimensional Gray-Scott model, utilizing measurements of the system state at a finite number of locations. Relations between the parameters of the model and the density of the sensor locations are derived that ensure the exponential convergence of the estimated state to the original one. The designed observer is capable of tracking a variety of complex spatiotemporal behaviors and self-replicating patterns. The theoretical findings are illustrated in particular numerical case studies. The results of the paper can be used for the synchronization analysis of the master–slave configuration of two identical Gray–Scott models coupled via a finite number of spatial points and can also be exploited for the purposes of feedback control applications in which the complete state information is required
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