Anti-Coherence Resonance

• Anti-coherence resonance is a phenomenon where noise or coupling induces maximal irregularity at intermediate parameter values, contrasting with coherence resonance.
• It is quantified using measures like the coefficient of variation in stochastic systems and correlation time in deterministic setups, highlighting system-specific extrema.
• The concept aids in understanding complex dynamics in excitable networks and chaotic oscillators, with applications ranging from neural models to electronic circuits.

Searching arXiv for recent and foundational papers on anti-coherence resonance and closely related suppression of coherence resonance. Anti-coherence resonance denotes a nonmonotonic loss of temporal regularity at an intermediate value of a control parameter, typically noise intensity or coupling strength, in systems that otherwise display coherence resonance or related noise-induced ordering. Across the recent literature, the term is used operationally rather than through a single universal definition: in stochastic excitable networks it is identified by a maximum of an interspike-interval variability measure, whereas in deterministic coupled chaotic oscillators it is identified by a minimum of correlation time. Closely related work also studies suppression of coherence resonance without always naming a distinct anti-coherence-resonance regime, which makes the topic partly terminological and partly metric-dependent (Masoliver et al., 2020, Baspinar et al., 2020, Komkov et al., 14 Sep 2025, Ryabov et al., 28 Jun 2025).

1. Conceptual definition

In the stochastic FitzHugh–Nagumo literature, coherence resonance is the appearance of maximally regular noise-induced spiking at an intermediate noise level, and anti-coherence resonance is its opposite in the sense that spiking becomes maximally irregular at an intermediate control parameter. In the multiplex neural-network formulation, the distinction is stated explicitly: coherence resonance corresponds to a pronounced minimum of the coefficient of variation of the interspike intervals, while anti-coherence resonance corresponds to a maximum of the same quantity as the noise intensity in another layer is varied (Masoliver et al., 2020).

In the deterministic Lorenz literature, the same conceptual opposition is retained but the observable changes. There, deterministic coherence resonance is a local maximum of correlation time, whereas deterministic anti-coherence resonance is a local minimum of correlation time as the coupling strength is varied. The phenomenon is therefore defined through coherence loss, not through the presence of external noise (Komkov et al., 14 Sep 2025).

This usage should be distinguished from two neighboring notions. First, “suppression of coherence resonance” may refer to a flattening or weakening of the coherence-resonance curves without the formal introduction of a separate anti-coherence-resonance branch. Second, “anti-resonance” in a parametrically excited Van der Pol oscillator refers to a deterministic minimum of oscillation amplitude at a special modulation frequency, not to a minimum of temporal coherence or a maximum of interspike irregularity (Ryabov et al., 28 Jun 2025, Chakraborty et al., 2012).

2. Diagnostic measures and operational criteria

The literature uses a small set of regularity measures. In stochastic excitable systems, the central observable is the coefficient of variation of interspike intervals,

$$R_k = \frac{\sigma^{ISI}_k}{\langle ISI \rangle_k},$$

or related population-averaged variants. In deterministic chaotic systems, the principal measure is the correlation time,

$$t_{\text{cor}}=\frac{1}{\Psi(0)}\int_0^\infty \left| \Psi(s) \right|ds,$$

sometimes normalized as

$$\tilde{t}_{\text{cor}}(K)=\frac{t_{\text{cor}}(K)}{t_{\text{cor}}(K=0)}.$$

A third class of work quantifies suppression of coherence resonance through a decrease of peak correlation time, an increase of the minimum normalized interspike-interval deviation, or a less pronounced spectral peak, but does not necessarily label the effect anti-coherence resonance (Masoliver et al., 2020, Baspinar et al., 2020, Komkov et al., 14 Sep 2025, Ryabov et al., 28 Jun 2025).

System class	Regularity measure	Anti-coherence signature
Multiplex FHN networks	$R_k=\sigma^{ISI}_k/\langle ISI\rangle_k$	Maximum of $R_k$
Global FHN mean-field/network model	$R(D)$ from ISI variability	Maximum of $R(D)$
Coupled Lorenz oscillators	$t_{\text{cor}}$, $\tilde t_{\text{cor}}$	Minimum of correlation time
Nonlocal-coupled FHN control	$\overline{t}_{\mathrm{cor}}$, $$t_{\text{cor}}=\frac{1}{\Psi(0)}\int_0^\infty \left| \Psi(s) \right|ds,$$0, $$t_{\text{cor}}=\frac{1}{\Psi(0)}\int_0^\infty \left| \Psi(s) \right|ds,$$1	Suppression of CR, not a formal ACR definition

A direct implication is that anti-coherence resonance is not tied to a single formula. It is tied to a local extremum of a system-specific regularity functional, with the extremum having the sign opposite to the one used for coherence resonance.

3. Noise-induced anti-coherence resonance in excitable networks

A direct stochastic realization appears in the two-layer multiplex neural-network model of excitable FitzHugh–Nagumo neurons. Each layer is a nearest-neighbor ring, all neurons are in the excitable regime with $$t_{\text{cor}}=\frac{1}{\Psi(0)}\int_0^\infty \left| \Psi(s) \right|ds,$$2 and $$t_{\text{cor}}=\frac{1}{\Psi(0)}\int_0^\infty \left| \Psi(s) \right|ds,$$3, and the two layers are weakly multiplexed with $$t_{\text{cor}}=\frac{1}{\Psi(0)}\int_0^\infty \left| \Psi(s) \right|ds,$$4. Layer 1 is driven by supra-threshold noise $$t_{\text{cor}}=\frac{1}{\Psi(0)}\int_0^\infty \left| \Psi(s) \right|ds,$$5, whereas layer 2 receives sub-threshold noise $$t_{\text{cor}}=\frac{1}{\Psi(0)}\int_0^\infty \left| \Psi(s) \right|ds,$$6 and is silent when $$t_{\text{cor}}=\frac{1}{\Psi(0)}\int_0^\infty \left| \Psi(s) \right|ds,$$7. In this setting, varying only $$t_{\text{cor}}=\frac{1}{\Psi(0)}\int_0^\infty \left| \Psi(s) \right|ds,$$8 can induce in layer 2 a sequence of coherence resonance, anti-coherence resonance, and inverse stochastic resonance. The anti-coherence branch is identified by a maximum of

$$t_{\text{cor}}=\frac{1}{\Psi(0)}\int_0^\infty \left| \Psi(s) \right|ds,$$9

at a higher $$\tilde{t}_{\text{cor}}(K)=\frac{t_{\text{cor}}(K)}{t_{\text{cor}}(K=0)}.$$0 than the coherence-resonance minimum (Masoliver et al., 2020).

The same paper attributes this behavior to a competition among three ingredients: noise-induced excitation in layer 1, weak signal transfer across layers, and the intrinsic excitability of the otherwise silent layer 2. At intermediate transferred drive, the perturbations arriving from layer 1 can induce comparatively regular spikes in layer 2; at other values of $$\tilde{t}_{\text{cor}}(K)=\frac{t_{\text{cor}}(K)}{t_{\text{cor}}(K=0)}.$$1, especially higher ones, the transferred fluctuations are strong enough to induce firing but too uneven to produce temporally regular responses. Anti-coherence resonance therefore denotes maximally irregular induced spiking, not simply weak firing.

The phenomenon is reported from the smallest multiplex pair up to large rings. Demonstrated network sizes include $$\tilde{t}_{\text{cor}}(K)=\frac{t_{\text{cor}}(K)}{t_{\text{cor}}(K=0)}.$$2. It is also robust to sparse inter-layer connectivity: for $$\tilde{t}_{\text{cor}}(K)=\frac{t_{\text{cor}}(K)}{t_{\text{cor}}(K=0)}.$$3, coherence resonance and anti-coherence resonance in layer 2 persist even when up to $$\tilde{t}_{\text{cor}}(K)=\frac{t_{\text{cor}}(K)}{t_{\text{cor}}(K=0)}.$$4 of inter-layer links are removed at random, and the extended material reports that for $$\tilde{t}_{\text{cor}}(K)=\frac{t_{\text{cor}}(K)}{t_{\text{cor}}(K=0)}.$$5 and $$\tilde{t}_{\text{cor}}(K)=\frac{t_{\text{cor}}(K)}{t_{\text{cor}}(K=0)}.$$6, coherence resonance and anti-coherence resonance can appear even with just one inter-layer link (Masoliver et al., 2020).

A second stochastic setting is the globally coupled FitzHugh–Nagumo population studied through both a network model and a mean-field limit. In the extended globally coupled formulation with noise in both equations, the regularity measure $$\tilde{t}_{\text{cor}}(K)=\frac{t_{\text{cor}}(K)}{t_{\text{cor}}(K=0)}.$$7 shows an ordinary coherence-resonance minimum at low or intermediate noise and an anti-coherence-resonance maximum at larger noise. For $$\tilde{t}_{\text{cor}}(K)=\frac{t_{\text{cor}}(K)}{t_{\text{cor}}(K=0)}.$$8, the minimum is reported near $$\tilde{t}_{\text{cor}}(K)=\frac{t_{\text{cor}}(K)}{t_{\text{cor}}(K=0)}.$$9 and the maximum near $R_k=\sigma^{ISI}_k/\langle ISI\rangle_k$0; for $R_k=\sigma^{ISI}_k/\langle ISI\rangle_k$1, the coherence-resonance minimum shifts to $R_k=\sigma^{ISI}_k/\langle ISI\rangle_k$2, while the anti-coherence maximum again occurs near $R_k=\sigma^{ISI}_k/\langle ISI\rangle_k$3. The proposed mechanism is that strong noise destroys the refractory-time structure of excitable firing and produces very small interspike intervals, so that firing becomes fluctuation-driven rather than governed by the intrinsic excursion-and-recovery cycle (Baspinar et al., 2020).

That result is not universal across all FHN reductions. The same paper states that the anti-coherence effect is robust in the extended globally coupled model, is not established for the locally coupled reduction, and is not a genuine network effect in the original globally coupled one-noise formulation, where a mean-field maximum is judged artificial (Baspinar et al., 2020).

4. Deterministic anti-coherence resonance

A qualitatively different realization appears in two bidirectionally coupled identical Lorenz oscillators,

$R_k=\sigma^{ISI}_k/\langle ISI\rangle_k$4

$R_k=\sigma^{ISI}_k/\langle ISI\rangle_k$5

$R_k=\sigma^{ISI}_k/\langle ISI\rangle_k$6

with $R_k=\sigma^{ISI}_k/\langle ISI\rangle_k$7, $R_k=\sigma^{ISI}_k/\langle ISI\rangle_k$8, and $R_k=\sigma^{ISI}_k/\langle ISI\rangle_k$9. Here there is no external noise. The control parameter is the coupling strength $R_k$0, and anti-coherence resonance is identified through a minimum of the correlation time of the $R_k$1-oscillations, while $R_k$2 and $R_k$3 simultaneously show deterministic coherence resonance through a maximum of correlation time (Komkov et al., 14 Sep 2025).

The effect occurs in the interval bounded by the onset of intermittent temporary synchronization at $R_k$4 and the onset of complete synchronization at $R_k$5. This is the on-off intermittency window, and the abstract characterizes it as hyperchaotic dynamics associated with the intermittency. Within that interval, the strongest deterministic coherence resonance in $R_k$6 and $R_k$7 occurs near $R_k$8, whereas the strongest deterministic anti-coherence resonance in $R_k$9 occurs near $R(D)$0. Experiments on an analog electronic model confirm the same qualitative structure, with the extrema shifted to $R(D)$1 and $R(D)$2 (Komkov et al., 14 Sep 2025).

This variable dependence is a distinctive feature. The same coupled chaotic attractor is reported as becoming more coherent in the $R(D)$3- and $R(D)$4-projections while becoming less coherent in the $R(D)$5-projection. The paper is explicit, however, that the theoretical reasons for the occurrence of deterministic coherence resonance and deterministic anti-coherence resonance are not clear and remain for further study (Komkov et al., 14 Sep 2025).

5. Suppression of coherence resonance and anti-coherence-like regimes

Several papers provide nearby phenomena that are directly relevant even when they avoid the term anti-coherence resonance. In a ring of $R(D)$6 noisy excitable FitzHugh–Nagumo oscillators with nonlocal coupling,

$R(D)$7

increasing the coupling radius can either enhance or suppress coherence resonance. The crucial case is strong coupling, $R(D)$8, where growth of the coupling radius suppresses coherence resonance: the peak of the averaged correlation time decreases, the minimum of the averaged normalized interspike-interval deviation increases, and the spectral peak becomes less favorable. The paper presents this as topology-induced suppression of coherence resonance rather than as a formally distinct anti-coherence-resonance state (Ryabov et al., 28 Jun 2025).

A similar constructive-to-destructive crossover appears in the excitable semiconductor superlattice driven by global voltage noise. There coherence resonance is identified by a minimum of

$R(D)$9

as external noise induces regular current self-oscillations through repeated nucleation and propagation of charge dipole waves from the injector. The paper does not use the term anti-coherence resonance, but it shows that after the coherence-resonance optimum, $R(D)$0 increases again, the spectra become less sharply organized, and in the ac-driven case the oscillations eventually lose frequency locking. These are anti-coherence-like deterioration branches beyond the optimum (Mompo et al., 2020).

An information-theoretic treatment of coherence resonance in a uni-junction transistor relaxation oscillator is relevant mainly by contrast. It associates the resonance regime with maximized differential entropy,

$R(D)$1

and maximized mutual information. That paper does not mention anti-coherence resonance explicitly. It only suggests, by implication, that departure from the resonance window would reduce periodicity, predictability, and effective information transfer (Rajhans et al., 2013).

6. Mechanisms, neighboring concepts, and unresolved issues

The mechanisms proposed for anti-coherence resonance differ by system class. In multiplex excitable networks, the phenomenon is linked to the mismatch between a noisy source layer and a silent target layer under weak multiplexing: transferred fluctuations can be regularizing at one noise level and maximally irregular at another. In globally coupled stochastic FHN populations, the anti-coherence branch is tied to strong-noise destruction of refractory-time organization and the appearance of very small interspike intervals. In coupled Lorenz oscillators, the relevant background is on-off intermittency and hyperchaotic dynamics below complete synchronization, but the paper explicitly leaves the detailed theory unresolved (Masoliver et al., 2020, Baspinar et al., 2020, Komkov et al., 14 Sep 2025).

Several common misconceptions are corrected by these results. Anti-coherence resonance is not merely “large noise gives disorder,” because the defining feature is a nonmonotonic extremum of a regularity measure. It is not necessarily a noise phenomenon, because deterministic anti-coherence resonance has been reported in the Lorenz system. It is also not identical to inverse stochastic resonance: in the multiplex FHN model, anti-coherence resonance is the maximum of $R(D)$2, whereas inverse stochastic resonance is a maximum of $R(D)$3, equivalently a minimum of firing rate (Masoliver et al., 2020).

It should also be separated from deterministic anti-resonance in parametrically excited nonlinear oscillators. In the Van der Pol system with parametrically excited nonlinearity,

$R(D)$4

anti-resonance means amplitude suppression of the stable self-oscillation at $R(D)$5, with

$R(D)$6

That is an amplitude minimum of a deterministic limit cycle, not a minimum of temporal coherence or a maximum of interspike irregularity (Chakraborty et al., 2012).

Taken together, the literature indicates that anti-coherence resonance is best understood as a family of coherence-loss phenomena defined operationally by the extremum of a regularity measure. The most mature direct realizations are the multiplex and globally coupled FitzHugh–Nagumo studies and the deterministic Lorenz study. The neighboring literature on suppression of coherence resonance, high-noise deterioration, and deterministic anti-resonance clarifies the boundaries of the concept, but also shows that its nomenclature remains system-dependent and still lacks a single canonical formulation (Ryabov et al., 28 Jun 2025, Mompo et al., 2020, Chakraborty et al., 2012).